☆ 4.6 Article

Conditioned random walks and interaction-driven condensation

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2017)

期刊

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

卷 50, 期 2, 页码 -

出版社

IOP PUBLISHING LTD

DOI: 10.1088/1751-8121/50/2/024005

关键词

random walk; condensation; large deviations; local time; zero-range process

类别

Physics, Multidisciplinary Physics, Mathematical

资金

EPSRC [EP/J007404/1]
EPSRC [EP/J007404/1] Funding Source: UKRI
Engineering and Physical Sciences Research Council [EP/J007404/1] Funding Source: researchfish

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Protocol

Reagent

摘要

We consider a discrete-time continuous-space random walk under the constraints that the number of returns to the origin (local time) and the total area under the walk are fixed. We first compute the joint probability of an excursion having area a and returning to the origin for the first time after time tau. We then show how condensation occurs when the total area constraint is increased: an excursion containing a finite fraction of the area emerges. Finally we show how the phenomena generalises previously studied cases of condensation induced by several constraints and how it is related to interaction-driven condensation which allows us to explain the phenomenon in the framework of large deviation theory.

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