4 papers
The largest fragment in self-similar fragmentation processes of positive index
Piotr Dyszewski, Samuel G. G. Johnston, Sandra Palau +1
We study a self-similar fragmentation process with dislocation measure and self-similarity index . Let denote the size of the largest fragment at time $t \ge…
Branching random walk and log-slowly varying tails
Ayan Bhattacharya, Piotr Dyszewski, Nina Gantert +1
We study a branching random walk with independent and identically distributed, heavy tailed displacements. The offspring law is supercritical and satisfies the Kesten-Stigum condit…
Random planar trees and the Jacobian conjecture
Elia Bisi, Piotr Dyszewski, Nina Gantert +3
We develop a probabilistic approach to the celebrated Jacobian conjecture, which states that any Keller map (i.e. any polynomial mapping who…
The extremal point process for branching random walk with stretched exponential displacements
Piotr Dyszewski, Nina Gantert
We investigate a branching random walk where the displacements are independent from the branching mechanism and have a stretched exponential distribution. We describe the positions…