Year: 2025
Type: preprint
Abstract: We prove that every directionally transient random walk in random i.i.d.\ environment, under condition $(T)_γ$, which admits an annealed functional limit towards Brownian motion also admits the corresponding quenched limit in $d \ge 2$. We exploit a classical strategy that was introduced by Bolthausen and Sznitman but, with respect to the existing literature, we get almost-optimal bounds on the variance of the quenched expectation of certain functionals of the random walk.
Source: arXiv (Cornell University)
Author: Scali, Carlo
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414875731
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