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1 Introduction In earlier lectures we mentioned that often a stochastic model is used for non-equilibrium systems In this case the deterministic variables represent slow system degrees of freedom while the noise represents the fast degrees of freedom In general the noise and the slow variables in such models are uncorrelated while different slow variables exhibit a temporal decorrelation
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Non-mainland China citizens cannot serve as both PI and international collaborator for NSFC programs at the same time The overseas collaborator of the International (Regional) Joint Research project (including Key International (Regional) Joint Research Program and International (Regional) Joint Research) shall not apply for other types of programs (except for the Research Fund for
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This is a slightly expanded version of the text of a lecture I gave in a conference at Rutgers University in honor of David Ruelle and Yasha Sinai In this lecture I reported on some of the main results surrounding an invariant measure introduced by Sinai, Ruelle and Bowen in the 1970s SRB measures, as these objects are called, play an important role in the ergodic theory of dissipative
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Preface These notes were developed for the course Probability and Statistics for Data Science at the Center for Data Science in NYU The goal is to provide an overview of fundamental concepts in probability and statistics from rst principles I would like to thank Levent Sagun and Vlad Kobzar, who were teaching assistants for the course, as well as Brett Bernstein and David Rosenberg for their
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n tends to a limit as n approaches in nity This lemma is quite crucial in the eld of subadditive ergodic theorems because it gives mathematicians some general ideas and guidelines in the non-random setting and leads to analogous discovery in the random setting Kingman's Subadditive Ergodic Theorem, for instance, is a perfect analogy in the random setting This paper will introduce Kingman's
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