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6 papers · 2 filters
Crossing probabilities in topological rectangles for the critical planar FK-Ising model
Dmitry Chelkak, Hugo Duminil-Copin, Clément Hongler
We consider the FK-Ising model in two dimensions at criticality. We obtain bounds on crossing probabilities of arbitrary topological rectangles, uniform with respect to the boundar…
On the approximation of convolutions by accompanying laws in the scheme of series
A. Yu. Zaitsev
The problem of the approximation of convolutions by accompanying laws in the scheme of series satisfying the infinitesimality condition is considered. It is shown that the quality…
Random walk with heavy tail and negative drift conditioned by its minimum and final values
Vincent Bansaye, Vladimir Vatutin
We consider random walks with finite second moment which drifts to and have heavy tail. We focus on the events when the minimum and the final value of this walk belong to…
A two-type Bellman--Harris process initiated by a large number of particles
Vladimir Vatutin, Alexander Iksanov, Valentin Topchii
We investigate a two-type critical Bellman--Harris branching process with the following properties: the tail of the life-length distribution of the first type particles is of order…
On the survival of a class of subcritical branching processes in random environment
Vincent Bansaye, Vladimir Vatutin
Let be the number of individuals in a subcritical BPRE evolving in the environment generated by iid probability distributions. Let be the logarithm of the expected offs…
On the probability that self-avoiding walk ends at a given point
Hugo Duminil-Copin, Alexander Glazman, Alan Hammond +1
We prove two results on the delocalization of the endpoint of a uniform self-avoiding walk on Z^d for d>1. We show that the probability that a walk of length n ends at a point x te…