The single ring theorem (2009)
Guionnet, Alice, Krishnapur, Manjunath, Zeitouni, Ofer
We study the empirical measure $L_{A_n}$ of the eigenvalues of non-normal square matrices of the form $A_n=U_nD_nV_n$ with $U_n,V_n$ independent Haar distributed on the unitary group and $D_n$ real...
Derivation of an eigenvalue probability density function relating to the Poincare disk (2009)
Forrester, Peter J., Krishnapur, Manjunath
A result of Zyczkowski and Sommers [J.Phys.A, 33, 2045--2057 (2000)] gives the eigenvalue probability density function for the top N x N sub-block of a Haar distributed matrix from U(N+n). In the...
My interests are in Probability theory, especially those parts that overlap with, and borrow from or contribute to other branches of Analysis. So far my research has been in the following topics: •...
Random matrices: Universality of ESDs and the circular law (2008)
Tao, Terence, Vu, Van, Krishnapur, Manjunath
Given an $n \times n$ complex matrix $A$, let $$\mu_{A}(x,y):= \frac{1}{n} |\{1\le i \le n, \Re \lambda_i \le x, \Im \lambda_i \le y\}|$$ be the empirical spectral distribution (ESD) of its...
1 Introduction Glauber Dynamics on Trees (2008)
Manjunath Krishnapur, Gábor Pete
This paper deals with Glauber dynamics for the Ising model on trees, with [5] as the primary reference. As explained below, Ising model on trees has an interpretation in terms of information
CS294-2 Markov Chain Monte Carlo: Foundations Applications Fall 2002 (2007)
Lecturer Alistair, Sinclair Scribes, Brian Milch, Manjunath Krishnapur
ith X 0 = x and Y 0 = y. We define the coupling as follows: X t and Y t both choose the same i and the same b at every step. Clearly this satisfies the two conditions (i) and (ii) in the above...
From random matrices to random analytic functions (2007)
We consider two families of random matrix-valued analytic functions: (1) G_1-zG_2 and (2) G_0 + zG_1 +z^2G_2+ ..., where G_i are n x n independent random matrices with independent standard complex...
Zeros of Random Analytic Functions (2006)
The dominant theme of this thesis is that random matrix valued analytic functions, generalizing both random matrices and random analytic functions, for many purposes can (and perhaps should) be...
Determinantal Processes and Independence (2006)
Hough, J. Ben, Krishnapur, Manjunath, Peres, Yuval, Virág, Bálint
We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics...
Overcrowding estimates for zeroes of Planar and Hyperbolic Gaussian analytic functions (2005)
We consider the point process of zeroes of certain Gaussian analytic functions and find the asymptotics for the probability that there are more than m points of the process in a fixed disk of radius...
Determinantal Processes and Independence (2005)
Hough, J. Ben, Krishnapur, Manjunath, Peres, Yuval, Virág, Bálint
We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics...
Recurrent Graphs where Two Independent Random Walks Collide Finitely Often (2004)
Krishnapur, Manjunath; University Of California At Berkeley, USA; Manju@stat.berkeley.edu, Peres, Yuval; University Of California At Berkeley, USA; Peres@stat.berkeley.edu
We present a class of graphs where simple random walk is recurrent, yet two independent walkers meet only finitely many times almost surely. In particular, the comb lattice, obtained from $Z^2$ by...
Recurrent graphs where two independent random walks collide finitely often (2004)
Krishnapur, Manjunath, Peres, Yuval
We present a class of graphs where simple random walk is recurrent, yet two independent walkers meet only finitely many times almost surely. In particular, the comb lattice, obtained from Z^2 by...