2016/08/31 by Juraj Szavits-Nossan, Martin R Evans, Martin R. Evans +2
Mathematics · Physics and Astronomy · #Condensation #Excursion #Large deviations theory #Mixing (physics) #Random walk #Stochastic process #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1751-8121/50/2/024005
published as 2017 J. Phys. A: Math. Theor. 50 024005 · 28 pages, 6 figures, invited paper for Special Issue of J. Phys. A "Emerging talents"
arxiv created 2016/10/21 · openalex publication_date 2016/12/07 · arxiv updated 2016/12/13 · openalex created_date 2016/12/16 · openalex updated_date 2026/08/05
Abstract 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 τ . 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.