1st CCDS Summer School on Random Matrix Theory

The Center for Computational & Data Sciences (CCDS) is organizing a 5-day summer school on “Random Matrix Theory” from 30th June to 4th July 2024.

Lecturer

Arijit Chakrabarty, PhD
Associate Professor
Theoretical Statistics and Mathematics Unit
Indian Statistical Institute
Kolkata, India
Website: Arijit Chakrabarty (isical.ac.in)

Place

Room#6002, BC, Independent University, Bangladesh

Schedule

• Lecture: 09:30 AM  – 11:00 AM
• Coffee Break :  11:00 AM – 11:30 AM
• Lecture:  11:30 AM – 01:00 PM
• Lunch: 01:00 PM – 02:30 PM

Lecture Plan

• Lecture 1: Basics of random matrices – Wigner and Wishart matrices, empirical spectral distribution, the method of moments, Stieltjes transform.
• Lecture 2: Convergence to the Wigner semicircle law – a complete proof via the method of moments.
• Lecture 3: Study of Wishart matrices, the convergence of the empirical spectral distribution to the Marchenko-Pastur law – a complete proof via Stieltjes transform.
• Lecture 4: The largest eigenvalue and eigenvector of perturbed random matrices with independent entries. Emphasis will be on finite rank perturbations.
• Lecture 5: Connections between random matrices and random graphs – study of the bulk and edge of the spectrum of the adjacency matrix.

Resources

Lecture notes from the school are available here.

Participants