Mini Course 1 - Timo Seppäläinen (Wisconsin)

Fluctuations for Particle Systems in One Dimension

Abstract:

These lectures investigate fluctuations of particle current in particle systems in one dimension that are asymmetric in the sense that the particles have an average drift in a particular direction. Two broad classes of systems with qualitatively distinct behavior are those with linear and those with strictly convex or concave flux functions. The flux function gives the average rate at which particle mass moves past a fixed location in space, as a function of average particle density. Examples with linear flux discussed in these lectures include independent walks (also in a random environment) and the random average process. Basic examples with concave flux include the asymmetric simple exclusion process and certain zero range processes.

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