Lectures on Probability Theory and Statistics Ecole d’Eté de Probabilités de Saint-Flour XXXII- 2002

	Author(s):	Boris Tsirelson, Wendelin Werner,Jean Picard
	Collection:	Lecture Notes in Mathematics 1840
	Publisher:	Springer-Verlag Berlin Heidelberg
	Year:	2004
	Language:	English
	Pages:	206 pages
	Size:	2.27 MB
	Extension:	PDF

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[content title="Description"]This is yet another indispensable volume for all probabilists and collectors of the Saint-Flour series, and is also of great interest for mathematical physicists. It contains two of the three lecture courses given at the 32nd Probability Summer School in Saint-Flour (July 7-24, 2002). Boris Tsirelson's lectures introduce the notion of nonclassical noise produced by very nonlinear functions of many independent random variables, for instance singular stochastic flows or oriented percolation. Two examples are examined (noise made by a Poisson snake, the Brownian web). A new framework for the scaling limit is proposed, as well as old and new results about noises, stability, and spectral measures. Wendelin Werner's contribution gives a survey of results on conformal invariance, scaling limits and properties of some two-dimensional random curves. It provides a definition and properties of the Schramm-Loewner evolutions, computations (probabilities, critical exponents), the relation with critical exponents of planar Brownian motions, planar self-avoiding walks, critical percolation, loop-erased random walks and uniform spanning trees.

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[content title="About the author"]Tsirelson was born in Leningrad to a Russian Jewish family. From his father Simeon's side, he is the great-nephew of rabbi Yehuda Leib Tsirelson, chief rabbi of Bessarabia from 1918 to 1941, and a prominent posek and Jewish leader. He obtained his Master of Science from the University of Leningrad and remained there to pursue graduate studies. He obtained his Ph.D. in 1975, with thesis "General properties of bounded Gaussian processes and related questions" written under the direction of Ildar Abdulovich Ibragimov.Jean Picard, (born July 21, 1620, La Flèche, Fr.—died July 12, 1682, Paris), French astronomer who first accurately measured the length of a degree of a meridian (longitude line) and from that computed the size of the Earth.

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