My Research
Book
Determining Spectra in Quantum Theory, Progress in Mathematical Physics Vol 44, Birkhauser, Boston, with M Demuth.
Mathematics
My Talks
-
Slides of talk given at Munich on AK Operators pdf file (July 2017).
-
Slides of talk given at UCI on Regularity of DOS for Random Schrodinger Operators pdf file (June 2019).
My Papers
-
On the local eigenvalue statistics for random band matrices in the localisation regime, with Peter Hislop, Preprint (2021)
-
Analyticity of the density of states for the Cauchy distribution, with Werner Kirsch, Preprint(2020).
-
Quantum Lattice Waveguides with Randomness - Localisation and Delocalisation, with Werner Kirsch , Preprint(2020).
-
Eigenvalue Statistics for Schrodinger Operators with random point interactions on R^d, d=1,2,3. pdf file with Peter Hislop, Werner Kirsch, Journal of Mathematical Physics, Vol 61, pp 92-103 (2020).
-
Regularity of Density of States of Random Schrodinger Operators pdf file with Dhriti Ranjan Dolai, Anish Mallick, To appear in Commun. Math. Phys, Vol 378(1), pp 299-328 (2020).
-
Szego's Theorem on the Lattice pdf file with Jitendriya Swain, Journal of Pseudo-Differential Operators and Applications, 10(2), 489-503 (2019) .
-
Decorrelation estimates for random Schr\"odinger operators with non rank one perturbations with P. D. Hislop and C. Shirley, Journal of Spectral Theory, 11(1), 63-89 (2021)
-
Global multiplicity bounds and Spectral Statistics for Random Operators , with Anish Mallick, Reviews in Mathematical Physics, Vol 32, No 9, 2050025 (2020).
-
Spectral Statistics for Anderson Model with sporadic potentials , with Werner Kirsch, Journal of Spectral Theory,Volume 10, Issue 2, pp. 581–597 (2020).
-
A Quantum Theory of Dark Matter pdf file Preprint(2016).
-
Persistence probabilities in centered, stationary, Gaussian Processes in discrete time pdf file with Manjunath Krishnapur, Indian Journal of Pure and Applied Mathematics, Vol 47(2), 183-194 (2016).
-
Eigengalue statistcs for random Schr\"odinger operators with non rank one potentials pdf file with Peter Hislop, Commun. Math. Phys. 340, 125-143(2015).
-
Poisson statistics in the Anderson model with singular randomness pdf file with Dhriti Ranjan Dolai, Journal of the Ramanujan Mathematical Society, Vol 30(3), (2015).
-
Level repulsion for a class of decaying random potentials pdf file with Dhriti Ranjan Dolai . Markov Processes and related fields, 21, 449-462 (2015) (a special issue on Leonid Pastur Festschrift).
-
A note on the analyticity of density of states pdf file with Masahiro Kaminaga, Shu Nakamura, Journal of Statistical Physics, November 2012, Volume 149, Issue 3, pp 496-504.
-
AC spectrum for a class of random operators at small disorder pdf file , Preprint (2011) (I will not publish this paper).
-
Absolutely continuous spectrum and spectral transition for some continuum random operators pdf file , Proc. Ind. Acad. Sci. Vol 122, (2) 243-255 (2012).
-
Direct Integrals and Spectral Averaging pdf file with Peter Stollmann, Journal of Operator Theory, 69(1), 101-107, (2013).
-
Lifshitz tails for the Interband Light Absorption Coefficient with W Kirsch and its pdf version. Proc. Ind. Acad. Sci. vol 120, no 4, 465-479 (2010) )
-
Regularity of the Interband Light Absorption Coefficient New version Oct 2009 - (original Nov 2008) and its pdf version. Proc. Ind. Acad. Sci. vol 120, No 3, pp 351-362 (2010).
-
Continuity of integrated density of states-independent randomness Proc. Ind. Acad. Sci., Vol 117(3), 401-410 (2007) pdf file
-
New criteria to identify spectrum with A Jensen, Proc. Ind. Acad. Sci, Vol 115(2), 217-226. pdf file
-
Extended abstract of talk given at Oberwolfach, May 2004 work with A Jensen. pdf file
-
Spectral and Dynamical properties of random models with nonlocal and singular interactions with P D Hislop and W Kirsch, Math. Nachrichten, 278(6), 627-664 (2005).
-
An Entropic Uncertainty Principle for Quantum Measurements with K R Parthasarathy, Sankhya, Series A, 64(3), 842-851 (2002).
-
Smoothness of density of states with random decaying interactions Proc. Ind. Acad. Sci. (Math Sci) 112(1), 163-181 (2002).
-
Convergence of Mann and Ishikawa iteration schemes for $\phi$- contractive maps in a Banach space. with G V R Babu (August 2000).
-
Improved convergence rate estimate of Ishikawa iteration process for Lipschitz strongly pseudocontractive maps in a Banach space., with G V R Babu, Bull. Cal. Math. Soc, 94(4), 253-258 (2002)).
-
Spectral properties of Anderson Type operators with decaying randomness with K B Sinha, Proc. Ind. Acad. Sci. (Math Sci) 111(2), 179-201 (2001).
-
Random Schrodinger operators with Wavelet interactions with W. Kirsch and P. Hislop, Wavelets and Allied Topics, Narosa Publishing House, New Delhi, (2001).
-
Localization and mobility edge for sparsely random potentials with J. Obermeit, IMSc Preprint IMSc 98/05/24 (corrected version) Oct 22, 1998.
-
Anderson Model with decaying randomness-mobility edge with W. Kirsch and J. Obermeit, Math. Z. 235(3), 421-433 (2000).
-
$\xi$-$\zeta$ relation , Proc. Ind. Acad. Sci 109(4), 379-383(1999).
-
Schrodinger operators with fairly arbitrary spectral features with V S Sunder, Rev. Math. Phys. 9 (No 3), 343-360(1997).
-
On isospectral sets of Jacobi operatorswith F Gesztesy and G Teschl, Commun.Math.Phys 181, 631-645(1996).
-
Inverse spectral theory for Jacobi matrices and their almost periodicity with Anand J Antony , Proc.Ind. Acad. Sci.Math.Sci 104(4) 777-818(1994).
-
Asymptotic analysis and the spectrum for Anyons with G Date and M V N Murthy, Int. Jour. Mod. Phys.A 9(15) 2545-2561 (1994)
-
Absolutely continuous spectrum for sparse potentials Proc. Ind. Acad. Sci. Math. Sci. 103(3) 333-339 (1993)
-
Almost periodicity of some random Jacobi matrices with Anand J Antony , Proc. Ind. Acad. Sci. Math. Sci. 102(3) 175-188 (1992)
-
Anderson model with decaying randomness-extended states Proc. Ind. Acad. Sci. Math. Sci 100(4) 285-294(1990)
-
Almost periodicity of some random potentials with S Kotani, Jour. Func. Ana. 78, 390-405(1987)
-
Large time behaviour of some N-body systems Commun. Math. Phys. 101, 129-152(1985)
-
On the completeness in three body scattering with Pl Muthuramalingam and K B Sinha, Ann. Inst. H. Poincare 41(1) 79-101(1984)
Finance
-
Value at Risk in the Indian Stock Markets with S K Shanthi, Indian Journal of Applied Finance, Vol 7 (4) (2001).
-
Stock price volatility and volume: a possible law with S K Shanthi, Preprint.
-
Stock price volatility and volume: A modified Black-Scholes formula with S K Shanthi.
Downloadable files are gzipped tex(latex2e/amstex) files.
My Research
Book
Determining Spectra in Quantum Theory, Progress in Mathematical Physics Vol 44, Birkhauser, Boston, with M Demuth.
Mathematics
My Talks
-
Slides of talk given at Munich on AK Operators pdf file (July 2017).
-
Slides of talk given at UCI on Regularity of DOS for Random Schrodinger Operators pdf file (June 2019).
My Papers
-
On the local eigenvalue statistics for random band matrices in the localisation regime, with Peter Hislop, Preprint (2021)
-
Analyticity of the density of states for the Cauchy distribution, with Werner Kirsch, Preprint(2020).
-
Quantum Lattice Waveguides with Randomness - Localisation and Delocalisation, with Werner Kirsch , Preprint(2020).
-
Eigenvalue Statistics for Schrodinger Operators with random point interactions on R^d, d=1,2,3. pdf file with Peter Hislop, Werner Kirsch, Journal of Mathematical Physics, Vol 61, pp 92-103 (2020).
-
Regularity of Density of States of Random Schrodinger Operators pdf file with Dhriti Ranjan Dolai, Anish Mallick, To appear in Commun. Math. Phys, Vol 378(1), pp 299-328 (2020).
-
Szego's Theorem on the Lattice pdf file with Jitendriya Swain, Journal of Pseudo-Differential Operators and Applications, 10(2), 489-503 (2019) .
-
Decorrelation estimates for random Schr\"odinger operators with non rank one perturbations with P. D. Hislop and C. Shirley, Journal of Spectral Theory, 11(1), 63-89 (2021)
-
Global multiplicity bounds and Spectral Statistics for Random Operators , with Anish Mallick, Reviews in Mathematical Physics, Vol 32, No 9, 2050025 (2020).
-
Spectral Statistics for Anderson Model with sporadic potentials , with Werner Kirsch, Journal of Spectral Theory,Volume 10, Issue 2, pp. 581–597 (2020).
-
A Quantum Theory of Dark Matter pdf file Preprint(2016).
-
Persistence probabilities in centered, stationary, Gaussian Processes in discrete time pdf file with Manjunath Krishnapur, Indian Journal of Pure and Applied Mathematics, Vol 47(2), 183-194 (2016).
-
Eigengalue statistcs for random Schr\"odinger operators with non rank one potentials pdf file with Peter Hislop, Commun. Math. Phys. 340, 125-143(2015).
-
Poisson statistics in the Anderson model with singular randomness pdf file with Dhriti Ranjan Dolai, Journal of the Ramanujan Mathematical Society, Vol 30(3), (2015).
-
Level repulsion for a class of decaying random potentials pdf file with Dhriti Ranjan Dolai . Markov Processes and related fields, 21, 449-462 (2015) (a special issue on Leonid Pastur Festschrift).
-
A note on the analyticity of density of states pdf file with Masahiro Kaminaga, Shu Nakamura, Journal of Statistical Physics, November 2012, Volume 149, Issue 3, pp 496-504.
-
AC spectrum for a class of random operators at small disorder pdf file , Preprint (2011) (I will not publish this paper).
-
Absolutely continuous spectrum and spectral transition for some continuum random operators pdf file , Proc. Ind. Acad. Sci. Vol 122, (2) 243-255 (2012).
-
Direct Integrals and Spectral Averaging pdf file with Peter Stollmann, Journal of Operator Theory, 69(1), 101-107, (2013).
-
Lifshitz tails for the Interband Light Absorption Coefficient with W Kirsch and its pdf version. Proc. Ind. Acad. Sci. vol 120, no 4, 465-479 (2010) )
-
Regularity of the Interband Light Absorption Coefficient New version Oct 2009 - (original Nov 2008) and its pdf version. Proc. Ind. Acad. Sci. vol 120, No 3, pp 351-362 (2010).
-
Continuity of integrated density of states-independent randomness Proc. Ind. Acad. Sci., Vol 117(3), 401-410 (2007) pdf file
-
New criteria to identify spectrum with A Jensen, Proc. Ind. Acad. Sci, Vol 115(2), 217-226. pdf file
-
Extended abstract of talk given at Oberwolfach, May 2004 work with A Jensen. pdf file
-
Spectral and Dynamical properties of random models with nonlocal and singular interactions with P D Hislop and W Kirsch, Math. Nachrichten, 278(6), 627-664 (2005).
-
An Entropic Uncertainty Principle for Quantum Measurements with K R Parthasarathy, Sankhya, Series A, 64(3), 842-851 (2002).
-
Smoothness of density of states with random decaying interactions Proc. Ind. Acad. Sci. (Math Sci) 112(1), 163-181 (2002).
-
Convergence of Mann and Ishikawa iteration schemes for $\phi$- contractive maps in a Banach space. with G V R Babu (August 2000).
-
Improved convergence rate estimate of Ishikawa iteration process for Lipschitz strongly pseudocontractive maps in a Banach space., with G V R Babu, Bull. Cal. Math. Soc, 94(4), 253-258 (2002)).
-
Spectral properties of Anderson Type operators with decaying randomness with K B Sinha, Proc. Ind. Acad. Sci. (Math Sci) 111(2), 179-201 (2001).
-
Random Schrodinger operators with Wavelet interactions with W. Kirsch and P. Hislop, Wavelets and Allied Topics, Narosa Publishing House, New Delhi, (2001).
-
Localization and mobility edge for sparsely random potentials with J. Obermeit, IMSc Preprint IMSc 98/05/24 (corrected version) Oct 22, 1998.
-
Anderson Model with decaying randomness-mobility edge with W. Kirsch and J. Obermeit, Math. Z. 235(3), 421-433 (2000).
-
$\xi$-$\zeta$ relation , Proc. Ind. Acad. Sci 109(4), 379-383(1999).
-
Schrodinger operators with fairly arbitrary spectral features with V S Sunder, Rev. Math. Phys. 9 (No 3), 343-360(1997).
-
On isospectral sets of Jacobi operatorswith F Gesztesy and G Teschl, Commun.Math.Phys 181, 631-645(1996).
-
Inverse spectral theory for Jacobi matrices and their almost periodicity with Anand J Antony , Proc.Ind. Acad. Sci.Math.Sci 104(4) 777-818(1994).
-
Asymptotic analysis and the spectrum for Anyons with G Date and M V N Murthy, Int. Jour. Mod. Phys.A 9(15) 2545-2561 (1994)
-
Absolutely continuous spectrum for sparse potentials Proc. Ind. Acad. Sci. Math. Sci. 103(3) 333-339 (1993)
-
Almost periodicity of some random Jacobi matrices with Anand J Antony , Proc. Ind. Acad. Sci. Math. Sci. 102(3) 175-188 (1992)
-
Anderson model with decaying randomness-extended states Proc. Ind. Acad. Sci. Math. Sci 100(4) 285-294(1990)
-
Almost periodicity of some random potentials with S Kotani, Jour. Func. Ana. 78, 390-405(1987)
-
Large time behaviour of some N-body systems Commun. Math. Phys. 101, 129-152(1985)
-
On the completeness in three body scattering with Pl Muthuramalingam and K B Sinha, Ann. Inst. H. Poincare 41(1) 79-101(1984)
Finance
-
Value at Risk in the Indian Stock Markets with S K Shanthi, Indian Journal of Applied Finance, Vol 7 (4) (2001).
-
Stock price volatility and volume: a possible law with S K Shanthi, Preprint.
-
Stock price volatility and volume: A modified Black-Scholes formula with S K Shanthi.
Downloadable files are gzipped tex(latex2e/amstex) files.
My Research
My Research
Book
Determining Spectra in Quantum Theory, Progress in Mathematical Physics Vol 44, Birkhauser, Boston, with M Demuth.
Mathematics
My Papers
-
Eigenfunctions and Quantum Transport with applications to trimmed Schrödinger Operators, with Peter Hislop and Werner Kirsch, Preprint (Jan 2024)
-
Regularity of the Integrated density of states in the continuous spectrum, Researchgate DOI: 10.13140/RG.2.2.23879.27044, to appear in Indian Journal of Pure and Applied Mathematics (issue devoted to Prof K R Parthasarathy).
-
Spectral Theory of some dark operators, with W Kirsch, preprint (2022), to appear in a conference proceedings.
-
Smoothness of density of states of the Anderson model on the Bethe lattice at high disorder with Dhriti Dolai, to appear in Journal of Statistical Physics, 190, 130 (2023).
-
On the local eigenvalue statistics for random band matrices in the localisation regime, with Peter Hislop, Journal of Statistical Physics, 187(3), June(2022).
-
Analyticity of the density of states for the Cauchy distribution, with Werner Kirsch, Preprint(2020).
-
Quantum Lattice Waveguides with Randomness - Localisation and Delocalisation, with Werner Kirsch , Annales Henri Poincare, 23, pages 4131–4148 (2022).
-
Eigenvalue Statistics for Schrodinger Operators with random point interactions on R^d, d=1,2,3. pdf file with Peter Hislop, Werner Kirsch, Journal of Mathematical Physics, Vol 61, pp 92-103 (2020).
-
Regularity of Density of States of Random Schrodinger Operators pdf file with Dhriti Ranjan Dolai, Anish Mallick, To appear in Commun. Math. Phys, Vol 378(1), pp 299-328 (2020).
-
Szego's Theorem on the Lattice pdf file with Jitendriya Swain, Journal of Pseudo-Differential Operators and Applications, 10(2), 489-503 (2019) .
-
Decorrelation estimates for random Schr\"odinger operators with non rank one perturbations with P. D. Hislop and C. Shirley, Journal of Spectral Theory, 11(1), 63-89 (2021)
-
Global multiplicity bounds and Spectral Statistics for Random Operators , with Anish Mallick, Reviews in Mathematical Physics, Vol 32, No 9, 2050025 (2020).
-
Spectral Statistics for Anderson Model with sporadic potentials , with Werner Kirsch, Journal of Spectral Theory,Volume 10, Issue 2, pp. 581–597 (2020).
-
A Quantum Theory of Dark Matter pdf file Preprint(2016).
-
Persistence probabilities in centered, stationary, Gaussian Processes in discrete time pdf file with Manjunath Krishnapur, Indian Journal of Pure and Applied Mathematics, Vol 47(2), 183-194 (2016).
-
Eigengalue statistcs for random Schr\"odinger operators with non rank one potentials pdf file with Peter Hislop, Commun. Math. Phys. 340, 125-143(2015).
-
Poisson statistics in the Anderson model with singular randomness pdf file with Dhriti Ranjan Dolai, Journal of the Ramanujan Mathematical Society, Vol 30(3), (2015).
-
Level repulsion for a class of decaying random potentials pdf file with Dhriti Ranjan Dolai . Markov Processes and related fields, 21, 449-462 (2015) (a special issue on Leonid Pastur Festschrift).
-
A note on the analyticity of density of states pdf file with Masahiro Kaminaga, Shu Nakamura, Journal of Statistical Physics, November 2012, Volume 149, Issue 3, pp 496-504.
-
AC spectrum for a class of random operators at small disorder pdf file , Preprint (2011) (I will not publish this paper).
-
Absolutely continuous spectrum and spectral transition for some continuum random operators pdf file , Proc. Ind. Acad. Sci. Vol 122, (2) 243-255 (2012).
-
Direct Integrals and Spectral Averaging pdf file with Peter Stollmann, Journal of Operator Theory, 69(1), 101-107, (2013).
-
Lifshitz tails for the Interband Light Absorption Coefficient with W Kirsch and its pdf version. Proc. Ind. Acad. Sci. vol 120, no 4, 465-479 (2010) )
-
Regularity of the Interband Light Absorption Coefficient New version Oct 2009 - (original Nov 2008) and its pdf version. Proc. Ind. Acad. Sci. vol 120, No 3, pp 351-362 (2010).
-
Continuity of integrated density of states-independent randomness Proc. Ind. Acad. Sci., Vol 117(3), 401-410 (2007) pdf file
-
New criteria to identify spectrum with A Jensen, Proc. Ind. Acad. Sci, Vol 115(2), 217-226. pdf file
-
Extended abstract of talk given at Oberwolfach, May 2004 work with A Jensen. pdf file
-
Spectral and Dynamical properties of random models with nonlocal and singular interactions with P D Hislop and W Kirsch, Math. Nachrichten, 278(6), 627-664 (2005).
-
An Entropic Uncertainty Principle for Quantum Measurements with K R Parthasarathy, Sankhya, Series A, 64(3), 842-851 (2002).
-
Smoothness of density of states with random decaying interactions Proc. Ind. Acad. Sci. (Math Sci) 112(1), 163-181 (2002).
-
Convergence of Mann and Ishikawa iteration schemes for $\phi$- contractive maps in a Banach space. with G V R Babu (August 2000).
-
Improved convergence rate estimate of Ishikawa iteration process for Lipschitz strongly pseudocontractive maps in a Banach space., with G V R Babu, Bull. Cal. Math. Soc, 94(4), 253-258 (2002)).
-
Spectral properties of Anderson Type operators with decaying randomness with K B Sinha, Proc. Ind. Acad. Sci. (Math Sci) 111(2), 179-201 (2001).
-
Random Schrodinger operators with Wavelet interactions with W. Kirsch and P. Hislop, Wavelets and Allied Topics, Narosa Publishing House, New Delhi, (2001).
-
Localization and mobility edge for sparsely random potentials with J. Obermeit, IMSc Preprint IMSc 98/05/24 (corrected version) Oct 22, 1998.
-
Anderson Model with decaying randomness-mobility edge with W. Kirsch and J. Obermeit, Math. Z. 235(3), 421-433 (2000).
-
$\xi$-$\zeta$ relation , Proc. Ind. Acad. Sci 109(4), 379-383(1999).
-
Schrodinger operators with fairly arbitrary spectral features with V S Sunder, Rev. Math. Phys. 9 (No 3), 343-360(1997).
-
On isospectral sets of Jacobi operatorswith F Gesztesy and G Teschl, Commun.Math.Phys 181, 631-645(1996).
-
Inverse spectral theory for Jacobi matrices and their almost periodicity with Anand J Antony , Proc.Ind. Acad. Sci.Math.Sci 104(4) 777-818(1994).
-
Asymptotic analysis and the spectrum for Anyons with G Date and M V N Murthy, Int. Jour. Mod. Phys.A 9(15) 2545-2561 (1994)
-
Absolutely continuous spectrum for sparse potentials Proc. Ind. Acad. Sci. Math. Sci. 103(3) 333-339 (1993)
-
Almost periodicity of some random Jacobi matrices with Anand J Antony , Proc. Ind. Acad. Sci. Math. Sci. 102(3) 175-188 (1992)
-
Anderson model with decaying randomness-extended states Proc. Ind. Acad. Sci. Math. Sci 100(4) 285-294(1990)
-
Almost periodicity of some random potentials with S Kotani, Jour. Func. Ana. 78, 390-405(1987)
-
Large time behaviour of some N-body systems Commun. Math. Phys. 101, 129-152(1985)
-
On the completeness in three body scattering with Pl Muthuramalingam and K B Sinha, Ann. Inst. H. Poincare 41(1) 79-101(1984)
Finance
-
Value at Risk in the Indian Stock Markets with S K Shanthi, Indian Journal of Applied Finance, Vol 7 (4) (2001).
-
Stock price volatility and volume: a possible law with S K Shanthi, Preprint.
-
Stock price volatility and volume: A modified Black-Scholes formula with S K Shanthi.
Downloadable files are gzipped tex(latex2e/amstex) files.