7 papers · 1 filter
Sharp concentration for the largest and smallest fragment in a -regular self-similar fragmentation
Piotr Dyszewski, Nina Gantert, Samuel G. G. Johnston +2
We study the asymptotics of the -regular self-similar fragmentation process. For and an integer , this is the Markov process in which each $I…
Large deviations for the maximum of a branching random walk with stretched exponential tails
Piotr Dyszewski, Nina Gantert, Thomas Höfelsauer
We prove large deviation results for the position of the rightmost particle, denoted by , in a one-dimensional branching random walk in a case when Cramér's condition is not s…
Homogeneous mappings of regularly varying vectors
Piotr Dyszewski, Thomas Mikosch
It is well known that the product of two independent regularly varying random variables with the same tail index is again regularly varying with this index. In this paper, we provi…
Random walks in a strongly sparse random environment
Dariusz Buraczewski, Piotr Dyszewski, Alexander Iksanov +1
The integer points (sites) of the real line are marked by the positions of a standard random walk. We say that the set of marked sites is weakly, moderately or strongly sparse depe…
Stable limit laws for random walk in a sparse random environment I: moderate sparsity
Dariusz Buraczewski, Piotr Dyszewski, Alexander Iksanov +2
A random walk in a sparse random environment is a model introduced by Matzavinos et al. [Electron. J. Probab. 21, paper no. 72: 2016] as a generalization of both a simple symmetric…
Precise large deviations for random walk in random environment
Dariusz Buraczewski, Piotr Dyszewski
We study one-dimensional nearest neighbour random walk in site-random environment. We establish precise (sharp) large deviations in the so-called ballistic regime, when the random…