Mathematics

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…

We study a critical multitype Bellman--Harris branching particle system in \(\mathbb R^N\) with a finite type space \(\mathbf K=\{1,\dots,K\}\). Particles of type \(I\) move according to a symmetric \(\alpha_i\)-stable process, have…

A result by N.G. Makarov [Algebra i Analiz, 1989] states that for martingales $(M_n)$ on the torus we have the strict inequality \[ \liminf_{n\to\infty} \frac{M_n}{\sum_{k=1}^n |\Delta M_k|} > 0 \] on a set of Hausdorff dimension one,…

We introduce a stochastic geometry dynamics inspired by opinion dynamics that captures the essence of modern asymmetric social networks with leaders and followers. Points in the Euclidean space represent opinions, and the leader of an agent…

We prove some results about the theory of independence in $\mathrm{NSOP}_{3}$ theories that do not hold in $\mathrm{NSOP}_{4}$ theories. We generalize Chernikov's work on simple and co-simple types in $\mathrm{NTP}_{2}$ theories to types…

We study the addition of two independent random $N\times M$ rectangular matrices with invariant distributions in two limiting regimes, where the parameter $\beta$ (inverse temperature) tends to infinity and $0$. In the low temperature…

In this work, we present the logistic branching Brownian motion with selection (Log-BBM), a modification of the N-BBM defined by Groisman et. al (2020), in which birth and competition events are decoupled to allow for a variable population…

We derive distributional approximations for the number of triangles in the linear preferential attachment model $\mathrm{PAM}(m,\delta)$, where $m\ge 2$ and $\delta>-m$, with explicit rates of convergence. The limiting distribution…

We prove asymptotic equivalents for finite-level representations of symmetric groups, that is, for Young diagrams having all but finitely many boxes on their first row. We deduce that random walks on symmetric groups generated by conjugacy…

Inspired by strict-monotonicity criteria for the time constant in first passage percolation, we investigate convex ordering of point processes in relation to the time constant in first contact percolation. In a nutshell, first contact…

We study the large-scale behaviour of a family of stochastic reaction-diffusion equations driven by long-range correlated noise in a weakly nonlinear regime. Depending on the decay of correlations of the noise and the strength of the…

In chapter 9 of his book "The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal", Woodin shows how to force the Strong Chang Conjecture over models of determinacy using $\mathbb{P}_{\mathrm{max}}$. We show here how a…