Theoretical Statistics and Mathematics Unit, ISI Delhi

January 17, 2018 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Anish Mallick,
ICTS-TIFR, Bangalore

Title:
Multiplicity of spectrum for certain class of random operators

Abstract of Talk

Random operators are an important field of study because of their role in
the theory of disordered media. One of the early models that used
randomness is the Anderson tight binding model, which was developed to
study spin wave diffusion in doped semiconductors. To study the random
operator is same as understanding the spectrum of the operator, and part of
the spectral theorem deals with multiplicity of the operator. In case of
Anderson type operator there are many results identifying pure point
spectrum and in some cases singular continuous and absolutely continuous
spectrum, but except for Anderson tight binding model multiplicity of
spectrum is unknown. Here we focus on the multiplicity problem for Anderson
type random operators and provide bound on multiplicity of singular
spectrum using the Green's function associated with each of the
perturbation (disorder is viewed as series of perturbation). In general
these type of result are false for fixed operator and these analysis works
because of disorder. Using the conclusions obtained, simplicity and bound
on multiplicity is also obtained for certain family of random operators.