My Book
Determining Spectra in Quantum Theory,
Progress in Mathematical Physics Vol 44, Birkhauser, Boston, with M Demuth.
My Papers
Mathematics
My Talks
Slides of talk given at Munich on AK Operators
pdf file (July 2017).
My Papers

A Quantum Theory of Dark Matter
pdf file Preprint.

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), 183194 (2016).

Decorrelation estimates for random Schrodinger operators with non rank one perturbatios
pdf file with Peter Hislop, Preprint (2015).

Eigengalue statistcs for random Schr\"odinger operators with non rank one potentials
pdf file with Peter Hislop, Commun. Math. Phys. 340, 125143(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, 449462 (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 496504.

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) 243255 (2012).

Direct Integrals and Spectral Averaging
pdf file with Peter Stollmann, Journal of Operator Theory, 69(1), 101107, (2013).

Szego's Theorem on the Lattice
pdf file with Jitendriya Swain, Preprint (2010).

Lifshitz tails for the Interband Light Absorption Coefficient
with W Kirsch and its pdf version. Proc. Ind. Acad. Sci. vol 120, no 4, 465479 (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 351362 (2010).

Continuity of integrated density of statesindependent
randomness
Proc. Ind. Acad. Sci., Vol 117(3), 401410 (2007)
pdf file

New criteria to identify spectrum
with A Jensen, Proc. Ind. Acad.
Sci, Vol 115(2), 217226.
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), 627664 (2005).

An Entropic Uncertainty Principle for Quantum Measurements
with K R Parthasarathy, Sankhya, Series A, 64(3),
842851 (2002).

Smoothness of density of states with random decaying
interactions Proc. Ind. Acad. Sci. (Math Sci) 112(1),
163181 (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),
253258 (2002)).

Spectral properties of Anderson Type operators with
decaying randomness
with K B Sinha, Proc. Ind. Acad. Sci. (Math Sci) 111(2),
179201 (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 randomnessmobility edge
with W. Kirsch and J. Obermeit, Math. Z. 235(3), 421433 (2000).

$\xi$$\zeta$ relation
, Proc. Ind. Acad. Sci 109(4), 379383(1999).

Schrodinger operators with fairly arbitrary spectral features
with V S Sunder, Rev. Math. Phys. 9 (No 3),
343360(1997).

On isospectral sets of
Jacobi operatorswith F Gesztesy and G Teschl,
Commun.Math.Phys 181, 631645(1996).
 Inverse spectral theory for Jacobi matrices and their
almost periodicity with Anand J Antony , Proc.Ind.
Acad. Sci.Math.Sci 104(4) 777818(1994).
 Asymptotic analysis and the spectrum for
Anyons with G Date and M V N Murthy, Int. Jour. Mod. Phys.A
9(15) 25452561 (1994)
 Absolutely continuous spectrum for sparse
potentials Proc. Ind. Acad. Sci. Math. Sci. 103(3)
333339 (1993)
 Almost periodicity of some random Jacobi
matrices with Anand J Antony , Proc. Ind. Acad. Sci. Math. Sci.
102(3) 175188 (1992)
 Anderson model with decaying randomnessextended
states Proc. Ind. Acad. Sci. Math. Sci 100(4) 285294(1990)
 Almost periodicity of some random potentials with S
Kotani, Jour. Func. Ana. 78, 390405(1987)
 Large time behaviour of some Nbody systems Commun.
Math. Phys. 101, 129152(1985)
 On the completeness in three body scattering
with Pl Muthuramalingam and K B Sinha,
Ann. Inst. H. Poincare 41(1) 79101(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 BlackScholes formula with S K Shanthi.
Downloadable files are gzipped tex(latex2e/amstex) files.