PDE and analysis seminar

Date

Thursday, March 7, 4 pm - 5 pm

Venue

Ramanujan Hall

Host

Chandan Biswas

speaker

Dhriti Ranjan Dolai

Affiliation

IIT Dharwad

Title

The central limit theorem (CLT) for integrated density of states (IDS) of discrete random Schrodinger operator (Anderson model on lattice)

Abstract

First, we will define the random Schrodinger operator on the Hilbert space of square summable functions on the d-dimensional integer lattice, and discuss its spectral properties. Also, we will talk about the integrated density of states (IDS). Now, we will consider the existence of the integrated density of states (IDS) as analogous to the law of large numbers (LLN). Then, we will prove the analogous central limit theorem (CLT) when test functions are either polynomials or first-order differentiable with polynomial growth.