Lab Home | Phone | Search
Center for Nonlinear Studies  Center for Nonlinear Studies
 Home 
 People 
 Current 
 Affiliates 
 Alumni 
 Visitors 
 Students 
 Research 
 ICAM-LANL 
 Quantum 
 Publications 
 Publications 
 2007 
 2006 
 2005 
 2004 
 2003 
 2002 
 2001 
 2000 
 <1999 
 Conferences 
 Workshops 
 Sponsorship 
 Talks 
 Colloquia 
 Colloquia Archive 
 Seminars 
 Postdoc Seminars Archive 
 Quantum Lunch 
 CMS Colloquia 
 Q-Mat Seminars 
 Q-Mat Seminars Archive 
 Archive 
 Kac Lectures 
 Dist. Quant. Lecture 
 Ulam Scholar 
 Colloquia 
 
 Jobs 
 Students 
 Summer Research 
 Student Application 
 Visitors 
 Description 
 Past Visitors 
 Services 
 General 
 PD Travel Request 
 
 History of CNLS 
 
 Maps, Directions 
 CNLS Office 
 T-Division 
 LANL 
 
Monday, March 16, 2015
10:00 AM - 11:00 AM
CNLS Conference Room (TA-3, Bldg 1690)

Colloquium

Detecting dynamics hidden in noise: Understanding phase transitions via statistical physics

Yue Lu
Harvard University

We consider the problem of distinguishing between two hypotheses: that a sequence of signals on a large graph consists entirely of noise, or that it contains the faint trail of a random walker buried in the noise. The problem of computing the error exponent of the optimal detector is simple to formulate, but exhibits deep connections to problems known to be difficult, such as computing Lyapunov exponents of products of random matrices and the free energy density of statistical mechanical systems with quenched disorder. By using random Hamiltonian interpolation, a technique previously applied in the rigorous analysis of spin glass systems, we show that a lower bound for the error exponent can be obtained by studying a generalized version of the random energy model, which is exactly soluble by large deviations techniques. Our bound closely matches the empirical results in numerical experiments, and it suggests a second-order phase transition phenomenon: below a threshold SNR, the error exponent is nearly constant and near zero, indicating poor performance; above the threshold, there is rapid improvement in performance as the SNR increases. The location of the phase transition depends on the entropy rate of the Markov processes. Finally, I will discuss cases where our lower bound is in fact asymptotically tight, in the limit of large state spaces of the underlying Markov processes.

Host: Misha Chertkov