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arXiv · 1808.00767

Self-interacting Brownian motion

Andras Suto
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Abstract

We prove a property of Brownian bridges whose certain time-equidistant sequences of points are pairwise coupled by an interaction. Roughly saying, if the total time span $t$ of the bridge tends to infinity while the distance of its end points is fixed or increases slower than $\sqrt{t}$, the process asymptotically forgets this distance, just as in the absence of interaction. The conclusion remains valid if the bridge interacts in a similar way also with another set of trajectories. The main example for the interaction is the Coulomb potential.

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Andras Suto. 2018-08-02. Self-interacting Brownian motion. https://arxiv.org/abs/1808.00767

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