Mathematics

Under the duality between the two-dimensional XY model and an integer-valued height function, the BKT transition is expected to correspond to the disappearance of a corner in the surface tension; in the delocalised phase, its zero-slope…

We give almost sure convergence rate bounds of ratio consensus algorithms when the protocol can be reformulated to be linear updates of vector values on a possibly larger, augmented network. This is an improvement of the results of…

We study sums of locally dependent scores associated with general marked (i.e., labeled) Euclidean point processes. We introduce geometric mixing conditions on the underlying point process and a Lipschitz-"localization" condition on the…

We study Brownian motion on Hermitian symmetric spaces of non-compact type in their bounded-domain realization. Using Jordan triple systems, we identify the spectral values after an appropriate change of variables as a Heckman-Opdam…

In the article the $mm$-entropy (an entropy of a metric measure space) introduced by C. Shannon is evaluated for an $\alpha$-stable L\'evy process. For $\alpha<1$ the double-sided estimates of the same order are obtained for process…

We establish scaling limit results for fluid dynamics equations driven by pseudo-transport noise. The behaviour of noise at small scales is governed by a parameter a. This extends previous results by Flandoli and Luo (2020) and Galeati…

We investigate the connection between Gaussian processes and Gaussian random elements in reproducing kernel Banach spaces. We show that the covariance operator of a weak second-order Radon probability measure on such a space is uniquely…

In this paper, we study discrete approximations of semi-Dirichlet forms obtained by adding non-symmetric drift terms, expressed in terms of mutual energy measures, to resistance forms whose associated resistance metric spaces are compact.…

In this paper, we investigate the asymptotic behavior of continuous-state branching processes in a Brownian random environment (CBBRE) conditioned on non-extinction. For the subcritical case, we prove the existence of the Yaglom limit and…

We study a system of $N$ inertial particles on a two-dimensional torus $\T^2$, evolving under a second-order stochastic dynamics with position-dependent friction $\lambda$ and noise amplitude $\sigma$, and undergoing coalescence at rate…

We derive a multidimensional Stein's method for asymptotic independence in the case of a general target $\mu$ with a density, being invariant measure of a diffusion process. It allows us to give a general bound in Wasserstein distance…

We prove precise almost sure lower path regularity results for a wide class of stochastic processes in all space dimensions $d\geq 1$. Examples include Gaussian processes, in particular, fractional Brownian motions with Hurst index $H\in…

We give a complete classification of the Jordan types occurring in the nilpotent commutator of a nilpotent matrix whose Jordan type is a hook partition. As a consequence, we also show that two partitions with the same generic commuting…

For a graded ideal I in a graded ring, the deviation of I is defined as the difference between the minimal number of generators of I and its grade. In this article, we provide bigraded free resolutions of the symmetric algebras for specific…

This short note presents a dimension-independent subgaussian concentration bound for Gaussian vectors under coordinate-wise nonlinear mappings. Discovered by Gemini 3.5 Flash, this result applies to any bounded function under a…

We show that the fields emerging from the log-determinant and the eigenvalue counting function of smooth Wigner matrices converge in law to centered Gaussian, logarithmically correlated, random elements in every negative Sobolev space…

We study a symmetry problem for the $h$-polynomials of edge rings of bipartite graphs. Let $G$ be a bipartite graph and write $h(\mathbb{k}[G];t)=h_0+h_1t+\cdots+h_st^s$. We prove that if $\Bbbk[G]$ is pseudo-Gorenstein and $h_1=h_{s-1}$,…

In this paper, we study the convergence rate between reflected backward stochastic differential equations with quadratic generators and their penalized BSDEs. Using techniques of BMO martingales, we prove the convergence rate is at order…

This note records a common threshold/surplus decomposition for single-threshold stopping rules in the classical prophet inequality. The same decomposition is used to certify several deterministic thresholds, including the median, half-mean,…

We study stochastic Burgers equation driven by a rough noise $(-\Delta)^{\gamma} dW_t$, where $\Delta$ is the Laplacian in one dimension with Dirichlet boundary conditions, and $\gamma \in [0,1/4)$. We prove exponential estimates for the…