Boris Tsirelson: Scaling Limit, Noise, Stability
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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.
Mathematics Subject Classification (2000):60-01 60Gxx 60J65 60K35 82B20 82b27 82B41
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