概率论
In this paper, we study fluctuation identities for spectrally negative L\'evy processes killed by a general class of additive functionals. We consider positive co-natural additive functionals (PcNAFs), which include as special cases both…
We study the topological structure of random geometric forests $G$ in the Euclidean plane under mild assumptions: non-crossing edges, stationarity, and finite edge intensity. The framework covers a broad range of constructions, including…
We study a Dirichlet--Ferguson process $\zeta$ on a general phase space. First we reprove the chaos expansion from Peccati (2008), providing an explicit formula for the kernel functions. Then we proceed with developing a Malliavin calculus…
Let $\nu_1,\nu_2,\dots$ be a sequence of probabilities on the nonnegative integers, and $X=(X_1,X_2, \dots)$ be a sequence of independent random variables $X_i$ with law $\nu_i$. For $\lambda>0$ denote $Z^\lambda_i:= \sum_x…
Let $f_n$ be a random polynomial of degree $n$ with i.i.d. mean-zero and finite variance random coefficients. It is well known that the roots of $f_n$ cluster uniformly around the unit circle as $n$ grows large. We give a simple and…
We derive non-linear stochastic Fokker-Planck equation from stochastic systems particles with individual and environmental noise via relative entropy method, with pathwise quantitative bounds. Moreover, we prove the existence of a unique…
Random geometric graphs defined on Euclidean subspaces, also called Gilbert graphs, are widely used to model spatially embedded networks across various domains. In such graphs, nodes are located at random in Euclidean space, and any two…
We strengthen the volume inequalities for L_p zonoids of even isotropic measures and for their duals, which are due to Ball, Barthe and Lutwak, Yang, Zhang. Along the way, we prove a stronger version of the Brascamp-Lieb inequality for a…
We present a tractable class of one-dimensional McKean-Vlasov equations that allow for unique strong solutions and extend the dynamics of various SIS epidemic models that are well-established in the literature. While the…
We study sequences of partitions of a non decreasing sequence I n of intervals into subintervals, starting from the trivial partition, in which each partition is obtained from the one before by splitting its subintervals in two, according…
This paper aims to extend the concept of stochastic $\Sigma$-convergence to the framework of Orlicz-Sobolev spaces in order to deals with coupled stochastic and deterministic homogenization problems in this type of spaces. Thus, this…
In this paper, we study the entrance measures of time-inhomogeneous McKean-Vlasov SDEs. The existence is obtained in great generality, where the system can be expanding globally and/or degenerate for numerous number of time intervals. When…
We consider a growing planar network where a tip grows at constant speed, branches at constant rate and inactivates when it meets a branch already created. We only consider here orthogonal branching occurring always in the same direction.…
This paper is concerned with a fluid-particle system given by the incompressible Navier-Stokes equations coupled with the Vlasov(-Fokker-Planck) equation through a drag force. Such a model arises naturally in the study of aerosols, sprays,…
Beckner's inequality is a family of inequalities that interpolates the two fundamental functional inequalities, the logarithmic Sobolev and Poincar\'e's inequalities. It is parametrized by exponent $p\in (1,2]$ and it implies the…
We disprove a conjecture stated in a recent paper by Arnold and Villasenor concerning the sum and the maximum of independent and identically distributed half-normal random variables. Our method is applicable to generalized gamma…
The Large Deviation Principle (LDP) and the Central Limit Theorem (CLT) are central pillars of probability theory. While their formulations are established under the i.i.d. assumption, the probabilistic foundation for power-law…
In this work, we analyse the effect of adding Gaussian white noise to the slow variable of a slow--fast system passing through a saddle--node (or fold) bifurcation. This problem is mainly motivated by applications to non-equilibrium energy…
We introduce a self-similar doubly stochastic Yule (DSY) cascade associated with the deterministic Navier-Stokes equations (NSE) in $\mathbb{R}^d$ with fractional dissipation $(-\Delta)^\gamma$. Interestingly, such a structure is…
In this paper, we study the expected value of the pair correlation statistics of randomized point configurations on the sphere, with the emphasis on point configurations generated by determinantal point processes. We study the cases of the…