2 citations · 2 across the 6 of their papers we have counts for
6 papers · 1 filter
On large deviations for the range of a two-dimensional random walk
Serguei Popov, Quirin Vogel
In this note, we compute the probability that a two-dimensional symmetric random walk visits more vertices than expected, for deviations on scales between the mean behavior and lin…
Phase Transitions in a Particle Model for the Self-Adaptive Response to Cancer Dynamics
Christian Kuehn, Quirin Vogel
In this paper, we present a probabilistic analysis of a dynamical particle model for the self-adaptive immune response to cancer, as proposed by the first author in a previous work…
1+O(1) asymptotics for loop percolation in five and higher dimensions
Quirin Vogel
We calculate the one-arm probability and the two-point function for loop percolation in dimensions five and higher on the lattice up to first order. This answers a question posed b…
Quenched critical percolation on Galton-Watson trees
Eleanor Archer, Quirin Vogel
We consider critical percolation on a supercritical Galton-Watson tree. We show that, when the offspring distribution is in the domain of attraction of an -stable law for some $…
A note on the intersections of two random walks in two dimensions
Quirin Vogel
In this note we prove a large deviation result for the intersection of the ranges of two independent random walks in dimension two. This complements the study of Phetpradap from 20…
Space-time random walk loop measures
Stefan Adams, Quirin Vogel
In this work, we investigate a novel setting of Markovian loop measures and introduce a new class of loop measures called Bosonic loop measures. Namely, we consider loop soups with…