Y. Velenik

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math.PR2025

Random Walk conditioned to stay above a non-flat floor: curvature effects

SÃ©bastien Ott, Yvan Velenik

Let $h : [0, 1] \to R$ be $C^{2}$ and such that $sup_{[0, 1]} h^{''} < 0$ . For a (large) positive integer $n$ , set $h_{n} (k) = nh (k / n)$ for any $k \in {0, \dots, n}$ . We consider a rando…

math.PR2025

Finite-time trajectorial estimates for inhomogeneous random walks

SÃ©bastien Ott, Yvan Velenik

We consider integer-valued random walks with independent but not identically distributed increments, and extend to this context several classical estimates, including a local limit…

math.PR2024

Fixed-magnetization Ising model with a slowly varying magnetic field

The motivation for this paper is the analysis of the fixed-density Ising lattice gas in the presence of a gravitational field. This is a seen as a particular instance of an Ising m…