On the Dynamical Evolution of the Arches Cluster (2009)
Chatterjee, Sourav, Goswami, Sanghamitra, Umbreit, Stefan, Glebbeek, Evert, Rasio, Frederic A., Hurley, Jarrod
We study the dynamical evolution of the young star cluster Arches and its dependence on the assumed initial stellar mass function (IMF). We perform many direct $N$-body simulations with various...
An observation about submatrices (2009)
Chatterjee, Sourav; University Of California At Berkeley; Sourav@stat.berkeley.edu, Ledoux, Michel; Institut De Mathematiques, Universite De Toulouse; Ledoux@math.univ-toulouse.fr
Let M be an arbitrary Hermitian matrix of order n, and k be a positive integer less than n. We show that if k is large, the distribution of eigenvalues on the real line is almost the same for almost...
Ethan Anderes, Sourav Chatterjee
This paper proves fixed domain asymptotic results for estimating a smooth invertible transformation f: R 2 → R 2 when observing the deformed random field Z ◦ f on a dense grid in a bounded simply...
Stein's Method of Exchangeable Pairs with Application to the Curie-Weiss Model (2009)
Chatterjee, Sourav, Shao, Qi-Man
Let $(W, W')$ be an exchangeable pair. Assume that $$E(W-W' | W) = g(W)+r(W),$$ where $g(W)$ is a dominated term and $r(W)$ is negligible. Let $G(t) = \int_0^t g(s) ds$ and define $p(t) = c_1 e^{-c_0...
AN OBSERVATION ABOUT SUBMATRICES (2009)
Sourav Chatterjee, Michel Ledoux
Abstract. Let M be an arbitrary Hermitian matrix of order n, and k be a positive integer ≤ n. We show that if k is large, the distribution of eigenvalues on the real line is almost the same for...
Disorder chaos and multiple valleys in spin glasses (2009)
We prove that the Sherrington-Kirkpatrick model of spin glasses is chaotic under small perturbations of the couplings at any temperature in the absence of an external field. The result is proved for...
Applications of Stein's method for concentration inequalities (2009)
Chatterjee, Sourav, Dey, Partha S.
Stein's method for concentration inequalities was introduced to prove concentration of measure in problems involving complex dependencies such as random permutations and Gibbs measures. In this...
Phase Transitions in Gravitational Allocation (2009)
Chatterjee, Sourav, Peled, Ron, Peres, Yuval, Romik, Dan
Given a Poisson point process of unit masses (``stars'') in dimension d>=3, Newtonian gravity partitions space into domains of attraction (cells) of equal volume. In earlier work, we showed the...
Unstable Planetary Systems Emerging Out Of Gas Disks (2009)
Matsumura, Soko, Thommes, Edward W., Chatterjee, Sourav, Rasio, Frederic A.
The discovery of over 300 extrasolar planets allows us to test our understanding of formation and dynamics of planetary systems statistically via numerical simulations. Traditional N-body simulations...
A combinatorial analysis of interacting diffusions (2009)
Chatterjee, Sourav, Pal, Soumik
We consider a particular class of n-dimensional homogeneous diffusions all of which have an identity diffusion matrix and a drift function that is piecewise constant and scale invariant. Abstract...
Limiting Spectral Distributions of Large Dimensional Random Matrices Arup Bose ∗ (2008)
Sourav Chatterjee, Sreela Gangopadhyay
Models where the number of parameters increases with the sample size, are becoming increasingly important in statistics. This necessitates a close look at the statistical properties of eigenvalues of...
Chaos, concentration, and multiple valleys (2008)
Disordered systems are an important class of models in statistical mechanics, having the defining characteristic that the energy landscape is a fixed realization of a random field. Examples include...
Central Limit Theorems for the Energy Density in the Sherrington-Kirkpatrick Model (2008)
Chatterjee, Sourav, Crawford, Nick
In this paper we consider central limit theorems for various macroscopic observables in the high temperature region of the Sherrington-Kirkpatrick spin glass model. With a particular focus on...
An observation about submatrices (2008)
Chatterjee, Sourav, Ledoux, Michel
Let M be an arbitrary Hermitian matrix of order n, and k be a positive integer less than or equal to n. We show that if k is large, the distribution of eigenvalues on the real line is almost the same...
A PHASE TRANSITION BEHAVIOR FOR BROWNIAN MOTIONS INTERACTING THROUGH THEIR RANKS (2008)
Abstract. Consider a time-varying collection of n points on the positive real axis, modeled as exponentials of n Brownian motions whose drift vector at every time point is determined by the relative...
Clearing the Dust from Globular Clusters (2008)
Umbreit, Stefan, Chatterjee, Sourav, Rasio, Frederic A.
Recent Spitzer observations of the globular cluster M15 detected dust associated with its intracluster medium. Surprisingly, these observations imply that the dust must be very short-lived compared...
Ethan Anderes, Sourav Chatterjee
This paper proves fixed domain asymptotic results for estimating a smooth invertible transformation f: R 2 → R 2 when observing the deformed random field Z ◦ f on a dense grid in a bounded simply...
A new approach to strong embeddings (2007)
We revisit strong approximation theory from a new perspective, culminating in a proof of the Komlos-Major-Tusnady embedding theorem for the simple random walk. The proof is almost entirely based on a...
Effects of stellar collisions on star cluster evolution and core collapse (2007)
Chatterjee, Sourav, Fregeau, John M., Rasio, Frederic A.
We systematically study the effects of collisions on the overall dynamical evolution of dense star clusters using Monte Carlo simulations over many relaxation times. We derive many observable...
Consistent Estimates of Deformed Isotropic Gaussian Random Fields on the Plane (2007)
Anderes, Ethan, Chatterjee, Sourav
This paper proves fixed domain asymptotic results for estimating a smooth invertible transformation $f\colon \Bbb R^2\to \Bbb R^2$ when observing the deformed random field $Z\circ f$ on a dense grid...
A phase transition behavior for Brownian motions interacting through their ranks (2007)
Chatterjee, Sourav, Pal, Soumik
Consider a time-varying collection of n points on the positive real axis, modeled as exponentials of n Brownian motions whose drift vector at every time point is determined by the relative ranks of...
Spin glasses and Stein's method (2007)
We introduce some applications of Stein's method in the high temperature analysis of spin glasses. Stein's method allows the direct analysis of the Gibbs measure without having to create a cavity....
Fluctuations of eigenvalues and second order Poincar\'e inequalities (2007)
Linear statistics of eigenvalues in many familiar classes of random matrices are known to obey gaussian central limit theorems. The proofs of such results are usually rather difficult, involving hard...
Dynamical Outcomes of Planet-Planet Scattering (2007)
Chatterjee, Sourav, Ford, Eric B., Matsumura, Soko, Rasio, Frederic A.
Observations in the past decade have revealed extrasolar planets with a wide range of orbital semimajor axes and eccentricities. Based on the present understanding of planet formation via core...
Multivariate normal approximation using exchangeable pairs (2007)
Chatterjee, Sourav, Meckes, Elizabeth
Since the introduction of Stein's method in the early 1970s, much research has been done in extending and strengthening it; however, there does not exist a version of Stein's original method of...
Gravitational allocation to Poisson points (2006)
Chatterjee, Sourav, Peled, Ron, Peres, Yuval, Romik, Dan
For d>=3, we construct a non-randomized, fair and translation-equivariant allocation of Lebesgue measure to the points of a standard Poisson point process in R^d, defined by allocating to each of the...
A new method of normal approximation (2006)
We introduce a new version of Stein's method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and...
A generalization of the Lindeberg principle (2006)
We generalize Lindeberg’s proof of the central limit theorem to an invariance principle for arbitrary smooth functions of independent and weakly dependent random variables. The result is applied to...
Exponential Approximation by Stein's Method and Spectral Graph Theory (2006)
Chatterjee, Sourav, Fulman, Jason, Rollin, Adrian
General Berry-Esseen bounds are developed for the exponential distribution using Stein's method. As an application, a sharp error term is obtained for Hora's result that the spectrum of the...
Estimation in spin glasses: A first step (2006)
The Sherrington--Kirkpatrick model of spin glasses, the Hopfield model of neural networks and the Ising spin glass are all models of binary data belonging to the one-parameter exponential family with...
Stein's method for concentration inequalities (2006)
We introduce a version of Stein's method for proving concentration and moment inequalities in problems with dependence. Simple illustrative examples from combinatorics, physics, and mathematical...
Dynamical Interactions of Planetary Systems in Dense Stellar Environments (2005)
Fregeau, John M., Chatterjee, Sourav, Rasio, Frederic A.
We study dynamical interactions of star--planet binaries with other single stars. We derive analytical cross sections for all possible outcomes, and confirm them with numerical scattering...
An error bound in the Sudakov-Fernique inequality (2005)
We obtain an asymptotically sharp error bound in the classical Sudakov-Fernique comparison inequality for finite collections of gaussian random variables. Our proof is short and self-contained, and...
Concentration of Haar measures, with an application to random matrices (2005)
We show that the mixing times of random walks on compact groups can be used to obtain concentration inequalities for the respective Haar measures. As an application, we derive a concentration...
A generalization of the Lindeberg principle (2005)
We generalize Lindeberg's proof of the central limit theorem to an invariance principle for arbitrary smooth functions of independent and weakly dependent random variables. The result is applied to...
A simple invariance theorem (2005)
We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin...
Concentration inequalities with exchangeable pairs (Ph.D. thesis) (2005)
The purpose of this dissertation is to introduce a version of Stein's method of exchangeable pairs to solve problems in measure concentration. We specifically target systems of dependent random...
Exchangeable pairs and Poisson approximation (2005)
Chatterjee, Sourav, Diaconis, Persi, Meckes, Elizabeth
This is a survey paper on Poisson approximation using Stein’s method of exchangeable pairs. We illustrate using Poisson-binomial trials and many variations on three classical problems of...
Concentration inequalities with exchangeable pairs / (2005)
Chatterjee, Sourav., Diaconis, Persi Advisor
Submitted to the Department of Statistics.
Exchangeable pairs and Poisson approximation (2004)
Chatterjee, Sourav, Diaconis, Persi, Meckes, Elizabeth
This is a survey paper on Poisson approximation using Stein's method of exchangeable pairs. We illustrate using Poisson-binomial trials and many variations on three classical problems of...