Related papers: Representations of Max-Stable Processes via Expone…
The Regularised Inertial Dean-Kawasaki model (RIDK) -- introduced by the authors and J. Zimmer in earlier works -- is a nonlinear stochastic PDE capturing fluctuations around the mean-field limit for large-scale particle systems in both…
We propose a systematic method to derive the asymptotic behaviour of the persistence distribution, for a large class of stochastic processes described by a general Fokker-Planck equation in one dimension. Theoretical predictions are…
We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper…
We consider a one-dimensional stationary time series of fixed duration $T$. We investigate the time $t_{\rm m}$ at which the process reaches the global maximum within the time interval $[0,T]$. By using a path-decomposition technique, we…
Three models from statistical physics can be analyzed by employing space-time determinantal processes: (1) crystal facets, in particular the statistical properties of the facet edge, and equivalently tilings of the plane, (2)…
We study the metastable dynamics of a discretised version of the mass-conserving stochastic Allen-Cahn equation. Consider a periodic one-dimensional lattice with $N$ sites, and attach to each site a real-valued variable, which can be…
In this paper, we study random dissipative weak solutions of the compressible Euler equations in the Kelvin-Helmholtz (KH) instability. Motivated by the fact that weak entropy solutions are not unique and can be viewed as inviscid limits of…
This paper develops some general calculus for GGC and Dirichlet process means functionals. It then proceeds via an investigation of positive Linnik random variables, and more generally random variables derived from compositions of a stable…
We present some product representations for random variables with the Linnik, Mittag-Leffler and Weibull distributions and establish the relationship between the mixing distributions in these representations. The main result is the…
We introduce and study a class of models of free fermions hopping between neighbouring sites with random Brownian amplitudes. These simple models describe stochastic, diffusive, quantum, unitary dynamics. We focus on periodic boundary…
The main goal of this paper is to construct a wavelet-type random series representation for a random field $X$, defined by a multistable stochastic integral, which generates a multifractional multistable Riemann-Liouville (mmRL) process…
Enhancing a recent result of Bayart and Ruzsa we obtain a Birkhoff-type characterization of upper frequently hypercyclic operators and a corresponding Upper Frequent Hypercyclicity Criterion. As an application we characterize upper…
Cluster random fields (CRFs) play a crucial role in the study of extremes of stationary regularly varying random fields (RFs). In particular, they appear in the Rosi\'nski representation of max-stable and $\alpha$-stable RFs. In this…
The extremal coefficient function (ECF) of a max-stable process $X$ on some index set $T$ assigns to each finite subset $A\subset T$ the effective number of independent random variables among the collection $\{X_t\}_{t\in A}$. We introduce…
We investigate a Poisson-Nernst-Planck type system in three spatial dimensions where the strength of the electric drift depends on a possibly small parameter and the particles are assumed to diffuse quadratically. On grounds of the global…
We analyse the asymptotic behaviour of solutions to the one dimensional fractional version of the porous medium equation introduced by Caffarelli and V\'azquez, where the pressure is obtained as a Riesz potential associated to the density.…
Max-stable distributions and processes are important models for extreme events and the assessment of tail risks. The full, multivariate likelihood of a parametric max-stable distribution is complicated and only recent advances enable its…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
By combining stability analysis of scalar field theories with the Darboux transformation technique, we create models featuring kink-like solutions whose quantum perturbations are all bounded. On the one hand, the stability analysis relates…
We present stability estimates for the inverse source problem of the stochastic Helmholtz equation in two and three dimensions by either near-field or far-field data. The random source is assumed to be a microlocally isotropic generalized…