概率论

We establish weighted Gaussian approximations for the uniform empirical and quantile processes and for their increments ending at a fixed point \(t\in(0,1)\). We first place the classical weighted approximations for the ordinary processes…

We identify necessary and sufficient conditions for a class of random mappings to send exchangeable $\{0,1\}$-sequences to other exchangeable $\{0,1\}$-sequences. We call this property the propagation of exchangeability, and show that any…

This paper studies the approximation of invariant distributions for a broad class of law-dependent dynamics, including McKean-Vlasov stochastic differential equations and Boltzmann-type equations. We consider discrete-time approximation…

Epidemic dynamics introduce time-varying heterogeneity into insured populations, as individuals' risk profiles depend on their evolving health status, thereby challenging classical insurance models based on homogeneity. Motivated by this…

Given a geometric statistic expressible as a sum of scores which depend on local data, \citet{BYY19} established central limit theorems for centered and normalized versions of these statistics, subject to the underlying point process having…

We introduce a unified framework via Stein's method for bounding the Kolmogorov distance between the generalized Dickman distributions and the distribution of randomly weighted sums of non-negative integer-valued random variables that are…

We study the inhomogeneous random graph with preferential attachment kernel and degree distribution with power-law exponent $\tau\in(2,3)$ as a representative of the class of graphs of preferential attachment type with infinite variance…

We develop an operator-algebraic framework for change-of-variables formulas on Wiener space, interpreting them as arising from hidden symmetries acting on observables. We show that general transformations can be represented by time-ordered…

We analyze the asymptotics of a block-Wishart random matrix ensemble of the type ${\boldsymbol W}_k = ({\boldsymbol X}^* \otimes {\boldsymbol I}_k){\boldsymbol T}({\boldsymbol X}\otimes{\boldsymbol I}_k)$ for ${\boldsymbol X}…

We study maximum-drawdown laws conditioned on extremes for a spectrally negative L\'evy process and observed up to an independent exponential time. The main contribution is a set of scale-function characterizations of the pre-infimum path…

We investigate a class of drift-based transformations between multidimensional diffusion processes. The approach allows to construct a new process whose transition probability density function (p.d.f.)\ can be expressed in a product form…

A recent breakthrough of Chen, Chen, Chen, Yin, and Zhang shows rapid mixing for Glauber dynamics for the hard-core model on random regular graphs beyond the tree uniqueness threshold. Their approach builds upon the literature of various…

We consider clusters formed by a Poisson ensemble of random walk loops on the $d$-regular tree with an intensity parameter $\alpha>0$ and a killing parameter $\kappa>-1$; the latter penalizes ($\kappa > 0$) or favors ($\kappa <0$) the…

In this paper, we give a short Bayesian proof of Talagrand's celebrated majorizing-measure theorem (MMT). While the upper-bound direction of MMT follows relatively directly from standard arguments, the lower-bound direction is widely…

We study Bernoulli percolation on $\mathbb Z^d$ in dimensions ${d>6}$. We prove that a classical consequence of the van den Berg-Kesten inequality, often referred to as the Simon-Lieb inequality in the context of the Ising model, admits a…

The renewal contact process is a non-Markovian variant of the classical contact process in which recoveries are governed by independent renewal processes with interarrival distribution $\mu$. We establish new sufficient conditions ensuring…

We derive closed form expressions for the lower expectations that correspond to total variation distance and chi-squared divergence balls around a probability mass function over a finite set.

We investigate integration by parts (IBP) formulae for stochastic Volterra equations and we establish the smoothing effect of the expectation. Due to the inherent path-dependent dynamics of this class of processes, standard…

Importance sampling (IS) consists in biasing samples from a distribution $f$ towards another distribution $g$. Concretely, given samples $X_i$ from $f$, the IS measure is $$\hat{g}_n = \frac{1}{Z_n}\sum_{i=1}^n \frac{g(X_i)}{f(X_i)}…

Using the Baxter-Kelland-Wu coupling and the convergence of the height function of the six-vertex model to the Gaussian Free Field, we extract critical exponents for the planar critical random-cluster model at $q=4$, and the planar…