Weakly self-avoiding walk in a random potential

24.10.2022, 13:00  –  Campus Golm, Haus 9, Raum 2.22
Forschungsseminar Wahrscheinlichkeitstheorie

Willem van Zuijlen (WIAS, Berlin)

We investigate a model of simple-random walk paths in a random environment that has two competing features: an attractive one towards the highest values of a random potential, and a self-repellent one in the spirit of the well-known weakly self-avoiding random walk. We tune the strength of the second effect such that they both contribute on the same scale as the time variable tends to infinity. In this talk I will discuss our results on the identification of (1) the logarithmic asymptotics of the partition function, and (2) of the path behaviour that gives the overwhelming contribution to the partition function. This is joint work with Wolfgang König, Nicolas Pétrélis and Renato Soares dos Santos. 

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