M. Baccara

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math.PR2026

On the range of competing random walks

Maxence Baccara

We consider $N$ independent random walks $X^{1}, \dots, X^{N}$ in the lattice $Z^{d}$ and prove limit theorems for the competitive range $R_{n}^{k}$ of the $k$ -th random wal…

math.PR2025

Functional Limit Theorems for the range of stable random walks

Maxence Baccara

In this paper we establish Functional Limit Theorems for the range of random walks in $Z^{d}$ that are in the domain of attraction of a non-degenerate $β$ -stable process in…