Carlo Scali

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math.PR2025

Collisions of random walks on comb graphs with a planar base

Umberto De Ambroggio, Maximilian Nitzschner, Carlo Scali

In this article we study collisions of two independent random walks on comb graphs $Comb (G ~, f)$ for a large class of recurrent planar graphs $G ~$ and profile…

math.PR2025

Quenched scaling limit for biased random walks on random, heavy tailed conductances: low dimensions

Umberto De Ambroggio, Carlo Scali

We consider a random walk amongst positive random conductances on $Z^{d}, d \geq 2$ , with directional bias. When the conductances have a stable distribution with parameter $Î…

math.PR2025

Quenched limit for diffusive biased random walks in random environment

Carlo Scali

We prove that every directionally transient random walk in random i.i.d.\ environment, under condition $(T)_{I^}^{3}$ , which admits an annealed functional limit towards Brownian motion a…

math.PR2024

Quenched invariance principle for biased random walks in random conductances in the sub-ballistic regime

Alexander Fribergh, Tanguy Lions, Carlo Scali

We consider a biased random walk in positive random conductances on $Z^{d}$ for $d \geq 5$ . In the sub-ballistic regime, we prove the quenched convergence of the properly res…