A. Fribergh

activity

20072025

most citedBiased random walks on random graphs

24 citations · 91 across the 18 of their papers we have counts for

collaborators

20 papers

math.PR2025

Bi-infinite incipient cluster in high dimensions

Manuel Cabezas, Alexander Fribergh, Markus Heydenreich +1

We consider high-dimensional percolation at the critical threshold. We condition the origin to be disjointly connected to two points, $x$ and $x^{'}$ , and subsequently take the limit…

math.PR2025

Scaling limit for the random walk on critical lattice trees

Gérard Ben Arous, Manuel Cabezas, Alexander Fribergh

We prove a scaling limit theorem for the simple random walk on critical lattice trees in $Z^{d}$ , for $d \geq 8$ . The scaling limit is the Brownian motion on the Integrated S…

math.PR2025

Random skeletons in high-dimensional lattice trees

Manuel Cabezas, Alexander Fribergh, Mark Holmes +1

We study the behaviour of the rescaled minimal subtree containing the origin and K random vertices selected from a random critical (sufficiently spread-out, and in dimensions d > 8…

math.PR2024

Sharp asymptotics for finite point-to-plane connections in supercritical bond percolation in dimension at least three

Alexander Fribergh, Alan Hammond

We consider supercritical bond percolation in $Z^{d}$ for $d \geq 3$ . The origin lies in a finite open cluster with positive probability, and, when it does, the diameter of…

math.PR2022★ 1 cited

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…

math.PR2020

Random Memory Walk

Alexander Fribergh, Daniel Kious, Vladas Sidoravicius +1

We present a simple model of a random walk with partial memory, which we call the \emph{random memory walk}. We introduce this model motivated by the belief that it mimics the beha…

math.PR2017

Backbone scaling limits for random walks on random critical trees

Gérard Ben Arous, Manuel Cabezas, Alexander Fribergh

We prove the existence of scaling limits for the projection on the backbone of the random walks on the Incipient Infinite Cluster and the Invasion Percolation Cluster on a regular…

math.PR2016★ 16 cited

Biased random walk on the interlacement set

Alexander Fribergh, Serguei Popov

We study a biased random walk on the interlacement set of $Z^{d}$ for $d \geq 3$ . Although the walk is always transient, we can show, in the case $d = 3$ , that for any value of…

math.PR2016★ 6 cited

Scaling limit for the ant in a simple labyrinth

Gérard Ben Arous, Manuel Cabezas, Alexander Fribergh

We prove that, after suitable rescaling, the simple random walk on the trace of a large critical branching random walk converges to the Brownian motion on the integrated super-Brow…

math.PR2016

Scaling limit for the ant in high-dimensional labyrinths

Gérard Ben Arous, Manuel Cabezas, Alexander Fribergh

We study here a detailed conjecture regarding one of the most important cases of anomalous diffusion, i.e the behavior of the "ant in the labyrinth". It is natural to conjecture (s…

math.PR2016

Scaling limits for sub-ballistic biased random walks in random conductances

Alexander Fribergh, Daniel Kious

We consider biased random walks in positive random conductances on the d-dimensional lattice in the zero-speed regime and study their scaling limits. We obtain a functional Law of…

math.PR2014★ 24 cited

Biased random walks on random graphs

Gerard Ben Arous, Alexander Fribergh

These notes cover one of the topics programmed for the St Petersburg School in Probability and Statistical Physics of June 2012. The aim is to review recent mathematical developmen…

math.PR2014

Local trapping for elliptic random walks in random environments in $Z^{d}$

Alexander Fribergh, Daniel Kious

We consider elliptic random walks in i.i.d. random environments on $Z^{d}$ . The main goal of this paper is to study under which ellipticity conditions local trapping occurs.…

math.PR2012

Biased random walk on critical Galton-Watson trees conditioned to survive

David A. Croydon, Alexander Fribergh, Takashi Kumagai

We consider the biased random walk on a critical Galton-Watson tree conditioned to survive, and confirm that this model with trapping belongs to the same universality class as cert…

math.PR2011★ 6 cited

A proof of the Lyons-Pemantle-Peres monotonicity conjecture for high biases

Gerard Ben Arous, Alexander Fribergh, Vladas Sidoravicius

The speed $v (β)$ of a $β$ -biased random walk on a Galton-Watson tree without leaves is increasing for $β \geq 717$ .

math.PR2011★ 6 cited

Biased random walk in positive random conductances on $Z^{d}$

Alexander Fribergh

We study the biased random walk in positive random conductances on $Z^{d}$ . This walk is transient in the direction of the bias. Our main result is that the random walk is…

math.PR2011★ 2 cited

Phase transition for the speed of the biased random walk on the supercritical percolation cluster

Alexander Fribergh, Alan Hammond

We prove the sharpness of the phase transition for speed in the biased random walk on the supercritical percolation cluster on Z^d. That is, for each d at least 2, and for any supe…

math.PR2008

The speed of a biased random walk on a percolation cluster at high density

Alexander Fribergh

We study the speed of a biased random walk on a percolation cluster on $Z^{d}$ in function of the percolation parameter $p$ . We obtain a first order expansion of the speed at $p = 1$ …

math.PR2008★ 21 cited

On slowdown and speedup of transient random walks in random environment

Alexander Fribergh, Nina Gantert, Serguei Popov

We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time $n$ th…

math.PR2007★ 9 cited

Biased random walks on a Galton-Watson tree with leaves

Gérard Ben Arous, Alexander Fribergh, Nina Gantert +1

We consider a biased random walk $X_{n}$ on a Galton-Watson tree with leaves in the sub-ballistic regime. We prove that there exists an explicit constant $γ = γ (β) \in (0, 1)$ , dependi…

Bi-infinite incipient cluster in high dimensions

Scaling limit for the random walk on critical lattice trees

Random skeletons in high-dimensional lattice trees

Sharp asymptotics for finite point-to-plane connections in supercritical bond percolation in dimension at least three

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

Random Memory Walk

Backbone scaling limits for random walks on random critical trees

Biased random walk on the interlacement set

Scaling limit for the ant in a simple labyrinth

Scaling limit for the ant in high-dimensional labyrinths

Scaling limits for sub-ballistic biased random walks in random conductances

Biased random walks on random graphs

Local trapping for elliptic random walks in random environments in Zd

Biased random walk on critical Galton-Watson trees conditioned to survive

A proof of the Lyons-Pemantle-Peres monotonicity conjecture for high biases

Biased random walk in positive random conductances on Zd

Phase transition for the speed of the biased random walk on the supercritical percolation cluster

The speed of a biased random walk on a percolation cluster at high density

On slowdown and speedup of transient random walks in random environment

Biased random walks on a Galton-Watson tree with leaves

Local trapping for elliptic random walks in random environments in $Z^{d}$

Biased random walk in positive random conductances on $Z^{d}$