Main Brownian Brownian motion. I
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Brownian Brownian motion. I

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A classical model of Brownian motion consists of a heavy molecule submerged into a gas of light atoms in a closed container. In this work the authors study a 2D version of this model, where the molecule is a heavy disk of mass M 1 and the gas is represented by just one point particle of mass m = 1, which interacts with the disk and the walls of the container via elastic collisions. Chaotic behavior of the particles is ensured by convex (scattering) walls of the container. The authors prove that the position and velocity of the disk, in an appropriate time scale, converge, as M, to a Brownian motion (possibly, inhomogeneous); the scaling regime and the structure of the limit process depend on the initial conditions. The proofs are based on strong hyperbolicity of the underlying dynamics, fast decay of correlations in systems with elastic collisions (billiards), and methods of averaging theory
Request Code : ZLIBIO1415940
Categories:
Year:
2009
Publisher:
Amer Mathematical Society
Language:
English
Pages:
208
ISBN 10:
082184282X
ISBN:
082184282X,978-0-8218-4282-9
Series:
Memoirs of the American Mathematical Society 0927

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