Conditioned random walks and interaction-driven condensation

Juraj Szavits-Nossan*, Martin R. Evans, Satya N. Majumdar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number024005
Number of pages28
JournalJournal of Physics A: Mathematical and Theoretical
Issue number2
Publication statusPublished - 7 Dec 2016


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


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