# My Research

Book

Determining Spectra in Quantum Theory, Progress in Mathematical Physics Vol 44, Birkhauser, Boston, with M Demuth.

Mathematics

My Papers

1. Spectral Theory of some dark operators, with W Kirsch, preprint (2022).

2. Smoothness of density of states of the Anderson model on the Bethe lattice at high disorder with Dhriti Dolai, preprint (2022).

3. On the local eigenvalue statistics for random band matrices in the localisation regime, with Peter Hislop, Preprint (2021) To appear in Journal of Statistical Physics.

4. Analyticity of the density of states for the Cauchy distribution, with  Werner Kirsch, Preprint(2020).

5. Quantum Lattice Waveguides with Randomness - Localisation and Delocalisation, with  Werner Kirsch , Preprint(2020) To appear in Annales Henri Poincare.

6. 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).

7. 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).

8. Szego's Theorem on the Lattice pdf file with Jitendriya Swain, Journal of Pseudo-Differential Operators and Applications, 10(2), 489-503 (2019) .

9. 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)

10. Global multiplicity bounds and Spectral Statistics for Random Operators , with Anish Mallick,  Reviews in Mathematical Physics, Vol 32, No 9, 2050025 (2020).

11. Spectral Statistics for Anderson Model with sporadic potentials , with Werner Kirsch,  Journal of Spectral Theory,Volume 10, Issue 2,  pp. 581–597 (2020).

12. A Quantum Theory of Dark Matter pdf file Preprint(2016).

13. 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).

14. Eigengalue statistcs for random Schr\"odinger operators with non rank one potentials pdf file with Peter Hislop, Commun. Math. Phys. 340, 125-143(2015).

15. 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).

16. 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).

17. 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.

18. AC spectrum for a class of random operators at small disorder pdf file , Preprint (2011) (I will not publish this paper).

19. Absolutely continuous spectrum and spectral transition for some continuum random operators pdf file , Proc. Ind. Acad. Sci. Vol 122, (2) 243-255 (2012).

20. Direct Integrals and Spectral Averaging pdf file with Peter Stollmann, Journal of Operator Theory, 69(1), 101-107, (2013).

21. 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) )

22. 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).

23. Continuity of integrated density of states-independent randomness Proc. Ind. Acad. Sci., Vol 117(3), 401-410 (2007)   pdf file

24. New criteria to identify spectrum with A Jensen, Proc. Ind. Acad. Sci, Vol 115(2), 217-226.   pdf file

25. Extended abstract of talk given at Oberwolfach, May 2004 work with A Jensen.   pdf file

26. 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).

27. An Entropic Uncertainty Principle for Quantum Measurements with K R Parthasarathy, Sankhya, Series A, 64(3), 842-851 (2002).

28. Smoothness of density of states with random decaying interactions Proc. Ind. Acad. Sci. (Math Sci) 112(1), 163-181 (2002).

29. Convergence of Mann and Ishikawa iteration schemes for $\phi$- contractive maps in a Banach space. with G V R Babu (August 2000).

30. 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)).

31. Spectral properties of Anderson Type operators with decaying randomness with K B Sinha, Proc. Ind. Acad. Sci. (Math Sci) 111(2), 179-201 (2001).

32. Random Schrodinger operators with Wavelet interactions with W. Kirsch and P. Hislop, Wavelets and Allied Topics, Narosa Publishing House, New Delhi, (2001).

33. Localization and mobility edge for sparsely random potentials with J. Obermeit, IMSc Preprint IMSc 98/05/24 (corrected version) Oct 22, 1998.

34. Anderson Model with decaying randomness-mobility edge with W. Kirsch and J. Obermeit, Math. Z. 235(3), 421-433 (2000).

35. $\xi$-$\zeta$ relation , Proc. Ind. Acad. Sci 109(4), 379-383(1999).

36. Schrodinger operators with fairly arbitrary spectral features with V S Sunder, Rev. Math. Phys. 9 (No 3), 343-360(1997).

37. On isospectral sets of Jacobi operatorswith F Gesztesy and G Teschl, Commun.Math.Phys 181, 631-645(1996).

38. 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).

39. 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)

40. Absolutely continuous spectrum for sparse potentials Proc. Ind. Acad. Sci. Math. Sci. 103(3) 333-339 (1993)

41. Almost periodicity of some random Jacobi matrices with Anand J Antony , Proc. Ind. Acad. Sci. Math. Sci. 102(3) 175-188 (1992)

42. Anderson model with decaying randomness-extended states Proc. Ind. Acad. Sci. Math. Sci 100(4) 285-294(1990)

43. Almost periodicity of some random potentials with S Kotani, Jour. Func. Ana. 78, 390-405(1987)

44. Large time behaviour of some N-body systems Commun. Math. Phys. 101, 129-152(1985)

45. On the completeness in three body scattering with Pl Muthuramalingam and K B Sinha, Ann. Inst. H. Poincare 41(1) 79-101(1984)

Finance

1. Value at Risk in the Indian Stock Markets with S K Shanthi, Indian Journal of Applied Finance, Vol 7 (4) (2001).

2. Stock price volatility and volume: a possible law with S K Shanthi, Preprint.

3. Stock price volatility and volume: A modified Black-Scholes formula with S K Shanthi.