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Superdiffusive bounds on self-repellent precesses in d = 2 — extended abstract

Bálint TóthBenedek Valkó — 2010

Actes des rencontres du CIRM

We prove superdiffusivity with multiplicative logarithmic corrections for a class of models of random walks and diffusions with long memory. The family of models includes the “true” (or “myopic”) self-avoiding random walk, self-repelling Durrett-Rogers polymer model and diffusion in the curl-field of (mollified) massless free Gaussian field in 2D. We adapt methods developed in the context of bulk diffusion of ASEP by Landim-Quastel-Salmhofer-Yau (2004).

Modeling flocks and prices: Jumping particles with an attractive interaction

Márton BalázsMiklós Z. RáczBálint Tóth — 2014

Annales de l'I.H.P. Probabilités et statistiques

We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle compared to the center of mass of the system. The rates are higher for those left behind, and lower for those ahead of the center of mass, providing an attractive interaction keeping the particles together. We prove that in the fluid limit, as the number of particles...

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