Related papers: Stable processes, self-similarity and the unit bal…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
Motivated by the formation of fingerprint patterns we consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations depend on an underlying tensor field. This class of models…
Given an infinitesimal perturbation of a discrete-time finite Markov chain, we seek the states that are stable despite the perturbation, \textit{i.e.} the states whose weights in the stationary distributions can be bounded away from $0$ as…
We consider a general honest homogeneous continuous-time Markov process with restarts. The process is forced to restart from a given distribution at time moments generated by an independent Poisson process. The motivation to study such…
Here we propose a different perspective of the deep factorisation in Kyprianou (2015) based on determining potentials. Indeed, we factorise the inverse of the MAP-exponent associated to a stable process via the Lamperti-Kiu transform. Here…
In this paper, we establish the existence of transition density for geometric $\alpha$-stable processes by using the property of self-decomposability--a fundamental concept in the theory of L\'evy processes. In contrast to traditional and…
In this note, we investigate the stability of self-similar blow-up solutions for superconformal semilinear wave equations in all dimensions. A central aspect of our analysis is the spectral equivalence of the linearized operators under…
Conditioning Markov processes to avoid a domain is a classical problem that has been studied in many settings. Ingredients for standard arguments involve the leading order tail asymptotics of the distribution of the first hitting time of…
A system consisting of the cubic complex Ginzburg-Landau equation which is linearly coupled to an additional linear dissipative equation, is considered. The model was introduced earlier in the context of dual-core nonlinear optical fibers…
Recently, it has been shown that stochastic spatial Lotka-Volterra models when suitably rescaled can converge to a super Brownian motion. We show that the limit process could be a super stable process if the kernel of the underlying motion…
We study products of random isometries acting on Euclidean space. Building on previous work of the second author, we prove a local limit theorem for balls of shrinking radius with exponential speed under the assumption that a Markov…
We develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based on and generalizes previous work by Abramovich-Polishchuk, Kuznetsov, Lieblich, and…
Studying the behaviour of Markov processes at boundary points of the state space has a long history, dating back all the way to William Feller. With different motivations in mind entrance and exit questions have been explored for different…
By killing a stable L\'{e}vy process when it leaves the positive half-line, or by conditioning it to stay positive, or by conditioning it to hit 0 continuously, we obtain three different positive self-similar Markov processes which…
An $\mathbb{R}^d$-valued Markov process $X^{(x)}_t=(X^{1,x_1}_t,\dots,X^{d,x_d}_t)$, $t\ge0,x\in\mathbb{R}^d$ is said to be multi-self-similar with index $(\alpha_1,\dots,\alpha_d)\in[0,\infty)^d$ if the identity in law…
This work presents an asymptotic stability result concerning the self-similar Blasius profiles $[\bar{u}, \bar{v}]$ of the stationary Prandtl boundary layer equation. Initially demonstrated by Serrin \cite{MR0282585}, the profiles…
We study the exponential dissipation of entropic functionals for continuous time Markov chains and the associated convex Sobolev inequalities, including MLSI and Beckner inequalities. We propose a method that combines the Bakry \'Emery…
In 1982 Macdonald published his now famous constant term conjectures for classical root systems. This paper begins with the almost trivial observation that Macdonald's constant term identities admit an extra set of free parameters, thereby…
Suppose that $\mathsf{S}$ is a closed set of the unit sphere $\mathbb{S}^{d-1} = \{x\in \mathbb{R}^d: |x| =1\}$ in dimension $d\geq2$, which has positive surface measure. We construct the law of absorption of an isotropic stable L\'evy…
In this article, we consider additive functionals $\zeta_t = \int_0^t f(X_s)\mathrm{d} s$ of a c\`adl\`ag Markov process $(X_t)_{t\geq 0}$ on $\mathbb{R}$. Under some general conditions on the process $(X_t)_{t\geq 0}$ and on the function…