概率论

We use the machinery of a conditional probability space (R\'enyi, 1955) to obtain an Agreement Theorem (Aumann, 1976) under general conditions. A conditional probability space (CPS) is a family of probability measures defined relative to a…

We consider $N\times N$ matrices $X$ with independent, identically distributed entries, and prove that the sequence of measures $\frac{ | \det (X-z)|^\gamma}{\mathbb{E}[ | \det (X-z)|^\gamma]}$ converge to the Gaussian Multiplicative Chaos…

The Wolff dynamics is a non-local Markov chain widely used for simulating the Ising model due to its effectiveness in reducing critical slowing down compared to the Glauber dynamics. Despite extensive algorithmic and numerical studies, a…

This paper investigates fractional Riesz-Bessel equations with random initial conditions that exhibit either classical or cyclic long-range dependence. It studies zoom-in asymptotics for the corresponding solutions and establishes…

Consider a sequence of random polynomials $P_n(z) = \prod_{k=1}^{n}(z - X_k)$, where $\{X_k\}_k$ are i.i.d. random variables distributed uniformly on the unit disc $\mathbb{D}$. Let $\Lambda_n = \{z \in \mathbb{C}: |P_n(z)| < 1\}$ be the…

We introduce a class of continuous Volterra processes, called Volterra clocks, and study their singular limit as the memory kernel collapses to a Dirac mass at zero. The dynamics are parametrised by a function $f$ acting as a nonlinear…

We investigate the impact on survival of a modification of the evolution of a sub-stochastic Markov chain that involves random relocations at previously visited states. Our central result is that such preferential relocations increase the…

We construct a continuous-time, positively divisible non-Markovian process with memory of the initial state that satisfies the differential Chapman--Kolmogorov equation. In the stationary state, the correlation function exhibits exponential…

We study second-order Consensus-Based Optimization (CBO), a derivative-free global optimization algorithm in which the consensus force and the multiplicative exploratory noise act on particle velocities. We prove quantitative…

In this paper, we solve exit problems for a L\'evy process that resets proportionally to its current position at independent Poisson epochs times. This resetting causes an additional (proportional to its current level) downward (upward)…

This paper studies the finite time explosion of the stochastic heat equation $\frac{\partial u}{\partial t}(t,x)=\frac{\partial^2}{\partial x^2} u(t,x)+(u(t,x))^{\beta}+\sigma(u(t,x))\dot{W}(t,x)$. We consider an interval $D=[-\pi,\pi]$…

We consider the configuration model and the uniform simple graph with given degree sequence $\boldsymbol{d}=\left(d_i\right)_{i=1}^n$. We derive quantitative bounds for the errors in (i) joint normal-Poisson approximation to the numbers of…

This paper studies how a fixed flexibility budget should be allocated across the two sides of a balanced bipartite matching market. We model compatibilities via a sparse bipartite stochastic block model in which flexible agents are more…

This paper derives noncentral limit theorems (NCLTs) for suitable scaling of functionals of spatially homogeneous and isotropic, and stationary in time, LRD Gaussian subordinated Spatiotemporal Random Fields (STRFs) with Hermite rank equal…

Adding the time as a component of a stochastic process before computing its signature terminal value ensures injectivity and supports universal approximation results, but it induces linear dependence among the components of the signature…

Similarity-sensitive entropy measures the uncertainty of a probability law relative to a similarity kernel that encodes the distinguishability between states. We develop a measure-theoretic treatment covering both finite similarity matrices…

This survey aims to review two decades of progress on exponential functionals of (possibly killed) real-valued L\'evy processes. Since the publication of the seminal survey by Bertoin and Yor, substantial advances have been made in…

This paper investigates extreme value theory for processes obtained by applying transformations to stationary Gaussian processes, also called subordinated Gaussian processes. The main contributions are as follows. First, we refine the…

We investigate the existence of a robust, i.e., continuous, representation of the conditional distribution in a stochastic filtering model for multidimensional correlated jump-diffusions. Even in the absence of jumps, it is known that in…

We analyse generating functions for trees and for connected subgraphs on the complete graph, and identify a single scaling profile which applies for both generating functions in a critical window. Our motivation comes from the analysis of…