Stochastic Deformations of Sample Paths of Random Walks and Exclusion Models

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dc.creatorFayolle, Guy
dc.creatorFurtlehner, Cyril
dc.date2006-03-09
dc.date.accessioned2026-07-07T07:02:17Z
dc.date.available2026-07-07T07:02:17Z
dc.descriptionThis study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion. Starting from examples, we give necessary and sufficient conditions for the underlying Markov processes to be reversible, in which case their invariant measure has a Gibbs form. Letting the size of the sample path increase, we find the convenient scalings bringing to light phase transition phenomena. Stable and metastable configurations are bound to time-periods of limiting deterministic trajectories which are solution of nonlinear differential systems: in the example of the ABC model, a system of Lotka-Volterra class is obtained, and the periods involve elliptic, hyper-elliptic or more general functions. Lastly, we discuss briefly the contour of a general approach allowing to tackle the transient regime via differential equations of Burgers' type.
dc.descriptionConference Proceedings, MathInfo2004, Vienna, 15 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/cond-mat/0603243
dc.identifierhttp://arxiv.org/abs/cond-mat/0603243
dc.identifierIn Mathematics and computer science. III, Trends Math., pages 415--428. Birkhäuser, Basel, 2004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/108547
dc.subjectStatistical Mechanics
dc.subjectOther Condensed Matter
dc.titleStochastic Deformations of Sample Paths of Random Walks and Exclusion Models
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