Student Probability Seminar

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Statics and dynamics of real-space condensation in the zero range process and related models

Speaker: Ori Hirschberg, CIMS

Location: Warren Weaver Hall 201

Date: Thursday, November 7, 2019, 12:15 p.m.

Synopsis:

Why do many cars concentrate during a traffic jam on a small stretch of a highway that may elsewhere seem open? How do some nodes in a complex network (e.g. websites in the internet) become “super hubs” linked to a macroscopic fraction of other nodes? These and similar phenomena are examples of real-space condensation: a phase transition in which a finite fraction of the “mass” in a macroscopic system is concentrated in a microscopic fraction of its volume. One of the simplest settings in which such condensation transitions can be studied is a model of stochastic interacting particles known as the zero range process (ZRP). In this talk I will review the ZRP and explain the origin of the condensation transition in the model. I will then discuss the dynamics of condensates in the ZRP and similar models, and present an unexpected feature recently discovered: spatial correlations in condensing systems may give rise to a collective motion of the condensate through the system.