Large deviation and hydrodynamic scaling. (English) Zbl 1006.60019

Varadhan, Srinivasa R. S.

Maruyama, Masaki (ed.) et al., Taniguchi conference on mathematics Nara ’98. Papers from the conference, Nara, Japan, December 15-20, 1998. Tokyo: Mathematical Society of Japan. Adv. Stud. Pure Math. 31, 265-286 (2001).

The author gives a very nice and pleasant introduction to large deviation and hydrodynamic scaling. A clear and easy introduction and some basic examples of the theory of large deviations are given as an introduction. In the second section hydrodynamic scaling is first discussed along the derivation of Euler equations from the equations of classical mechanics. Then the simple exclusion process on the integer lattice \( \mathbb Z^d \) with its hydrodynamics is explained focusing on the main ideas. In the remaining two sections important questions of the hydrodynamic scaling and large deviation methods in hydrodynamic scaling are explained without any technical proof. This text provides beside a gentle introduction to the main ideas further references for reading.
For the entire collection see [Zbl 0980.00032].

Reviewer: Stefan Adams (Berlin)

MSC:

60F10	Large deviations
60K35	Interacting random processes; statistical mechanics type models; percolation theory
82B41	Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
60G50	Sums of independent random variables; random walks
82C22	Interacting particle systems in time-dependent statistical mechanics

Keywords:

large deviation; Euler equation; hydrodynamic scaling; simple exclusion