Marek Biskup

activity

20002025

most citedA central limit theorem for the effective conductance: Linear boundary data and small ellipticity contrasts

20 citations · 20 across the 5 of their papers we have counts for

collaborators

5 papers

math.PR2025

Extremal properties of the random walk local time

Marek Biskup

These are expanded lecture notes for a minicourse taught at the "School on disordered media" at the Alfred Renyi institute in Budapest, January 2025.

math.PR2024

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models

Marek Biskup, Haiyu Huang

Given a square box $Λ_{n} \subseteq Z^{2}$ of side length $L^{n}$ with $L, n > 1$ , we study hierarchical random fields ${ϕ_{x} : x \in Λ_{n}}$ with law proportional to ${\rm e}^{\frac…

math.PR2023

A limit law for the maximum of subcritical DG-model on a hierarchical lattice

Marek Biskup, Haiyu Huang

We study the extremal properties of the "integer-valued Gaussian" a.k.a.\ DG-model on the hierarchical lattice $Λ_{n} := {1, \dots, b}^{n}$ (with $b \geq 2$ ) of depth $n$ . This is a random…

math.PR2012★ 20 cited

A central limit theorem for the effective conductance: Linear boundary data and small ellipticity contrasts

Marek Biskup, Michele Salvi, Tilman Wolff

Given a resistor network on $Z^{d}$ with nearest-neighbor conductances, the effective conductance in a finite set with a given boundary condition is the the minimum of the Di…

math-ph2000

Long-time tails in the parabolic Anderson model with bounded potential

Marek Biskup, Wolfgang Koenig

We consider the parabolic Anderson problem $\partial_{t} u = κ Δ u + ξ u$ on $(0, \infty) \times Z^{d}$ with random i.i.d. potential $ξ = (ξ (z))_{z \in Z^{d}}$ and the initial condition $u(0,\cdot)…