Zobrazeno 1 - 10
of 54
pro vyhledávání: '"Dyszewski, P."'
Take a self-similar fragmentation process with dislocation measure $\nu$ and index of self-similarity $\alpha > 0$. Let $e^{-m_t}$ denote the size of the largest fragment in the system at time $t\geq 0$. We prove fine results for the asymptotics of t
Externí odkaz:
http://arxiv.org/abs/2409.11795
We study a branching random walk with independent and identically distributed, heavy tailed displacements. The offspring law is supercritical and satisfies the Kesten-Stigum condition. We treat the case when the law of the displacements does not lie
Externí odkaz:
http://arxiv.org/abs/2404.17953
Autor:
Bisi, Elia, Dyszewski, Piotr, Gantert, Nina, Johnston, Samuel G. G., Prochno, Joscha, Schmid, Dominik
We develop a probabilistic approach to the celebrated Jacobian conjecture, which states that any Keller map (i.e. any polynomial mapping $F\colon \mathbb{C}^n \to \mathbb{C}^n$ whose Jacobian determinant is a nonzero constant) has a compositional inv
Externí odkaz:
http://arxiv.org/abs/2301.08221
We study the quenched behaviour of a perturbed version of the simple symmetric random walk on the set of integers. The random walker moves symmetrically with an exception of some randomly chosen sites where we impose a random drift. We show that if t
Externí odkaz:
http://arxiv.org/abs/2301.00478
Autor:
Dyszewski, Piotr, Gantert, Nina
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 of the particles in the vicinity of the rightmost particle in terms o
Externí odkaz:
http://arxiv.org/abs/2212.06639
Publikováno v:
Stochastic Processes and Their Applications, 159 (2023), pp. 199-224
We study a class of kinetic-type differential equations $\partial \phi_t/\partial t+\phi_t=\widehat{\mathcal{Q}}\phi_t$, where $\widehat{\mathcal{Q}}$ is an inhomogeneous smoothing transform and, for every $t\geq 0$, $\phi_t$ is the Fourier--Stieltje
Externí odkaz:
http://arxiv.org/abs/2208.09498
We study the asymptotics of the $k$-regular self-similar fragmentation process. For $\alpha > 0$ and an integer $k \geq 2$, this is the Markov process $(I_t)_{t \geq 0}$ in which each $I_t$ is a union of open subsets of $[0,1)$, and independently eac
Externí odkaz:
http://arxiv.org/abs/2102.08935
We prove large deviation results for the position of the rightmost particle, denoted by $M_n$, in a one-dimensional branching random walk in a case when Cram\'er's condition is not satisfied. More precisely we consider step size distributions with st
Externí odkaz:
http://arxiv.org/abs/2006.09207
We study the one-dimensional branching random walk in the case when the step size distribution has a stretched exponential tail, and, in particular, no finite exponential moments. The tail of the step size $X$ decays as $\mathbb{P}[X \geq t] \sim a \
Externí odkaz:
http://arxiv.org/abs/2004.03871
Autor:
Dyszewski, Piotr, Mikosch, Thomas
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 provide sharp sufficient conditions for the regular variation property of p
Externí odkaz:
http://arxiv.org/abs/1903.11010