Boris Tsirelson
Published 2003-01-21Version 1
Linear functions of many independent random variables lead to classical noises (white, Poisson, and their combinations) in the scaling limit. Some singular stochastic flows and some models of oriented percolation involve very nonlinear functions and lead to nonclassical noises. Two examples are examined, Warren's `noise made by a Poisson snake' and the author's `Brownian web as a black noise'. Classical noises are stable, nonclassical are not. A new framework for the scaling limit is proposed. Old and new results are presented about noises, stability, and spectral measures.
Comments: A summer school course, 108 pages, 42 small figs
Journal: Lect. Notes Math. 1840 (2004), 1-106.
On the Expectations of Maxima of Sets of Independent Random Variables
Concentration and Moment Inequalities for Polynomials of Independent Random Variables
Independent random variables on Abelian groups with independent the sum and difference
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