## The random walk penalised by its range in dimensions $d\geq 3$

*Berestycki, Nathanael*;

*Cerf, Raphael*;

- Subject: Mathematics - Probabilityarxiv: Mathematics::Probability

We study a self-attractive random walk such that each trajectory of length $N$ is penalised by a factor proportional to $\exp ( - |R_N|)$, where $R_N$ is the set of sites visited by the walk. We show that the range of such a walk is close to a solid Euclidean ball of ra... View more

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