相关论文: Quasi-symmetries and rigidity for determinantal po…

We consider determinantal point processes on the $d$-dimensional unit sphere $\mathbb S^d$. These are finite point processes exhibiting repulsiveness and with moment properties determined by a certain determinant whose entries are specified…

Recently Gambaudo and Ghys proved that there exist infinitely many quasi-morphisms on the group ${\rm Diff}_\Omega^\infty (D^2, \partial D^2)$ of area-preserving diffeomorphisms of the 2-disk $D^2$. For the proof, they constructed a…

We study fundamental properties of the gamma process and their relation to various topics such as Poisson-Dirichlet measures and stable processes. We prove the quasi-invariance of the gamma process with respect to a large group of linear…

We consider the behavior of spatial point processes when subjected to a class of linear transformations indexed by a variable T. It was shown in Ellis [Adv. in Appl. Probab. 18 (1986) 646-659] that, under mild assumptions, the transformed…

We study point processes on the real line whose configurations $X$ are locally finite, have a maximum and evolve through increments which are functions of correlated Gaussian variables. The correlations are intrinsic to the points and…

We study the structure of invariant measures for continuous automorphisms of compact metrizable abelian groups satisfying the descending chain condition. We show that the finitely supported invariant measures are weak-* dense in the space…

In this paper, we consider a quasi-linear Dirichlet system with possible competing $(p,q)$-Laplacians and convections. Due to the lack of ellipticity, monotonicity, and variational structure, the standard approaches to the existence of weak…

We study the surjectivity of the Cauchy-Riemann and Laplace operators on certain weighted spaces of smooth functions of rapid decay on strip-like domains in the complex plane that are defined via weight function systems. We fully…

This article investigates the phenomenon of maximal rigidity in spatial processes, where perfect interpolation of the process is possible from partial information, specifically, from its restriction to a strict subdomain, often resulting in…

In this paper, we study the full asymptotic expansion of the partition functions of determinantal point processes defined on a polarized K\"ahler manifold. We show that the coefficients of the expansion are given by geometric functionals on…

We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. ``Quasi-stationary states'' are defined as probability measures, on the \sigma-algebra generated by the gap variables,…

The Bernstein approximation problem is to determine whether or not the space of all polynomials is dense in a given weighted $C_0$-space on the real line. A theorem of L. de Branges characterizes non--density by existence of an entire…

Higher-spin diffeomorphisms are to higher-order differential operators what diffeomorphisms are to vector fields. Their rigorous definition is a challenging mathematical problem which might predate a better understanding of higher-spin…

Two groups are virtually isomorphic if they can be obtained one from the other via a finite number of steps, where each step consists in taking a finite extension or a finite index subgroup (or viceversa). Virtually isomorphic groups are…

We characterize finite sets $S$ of nonwandering points for generic diffeomorphisms $f$ as those which are {\em uniformly bounded}, i.e., there is an uniform bound for small perturbations of the derivative of $f$ along the points in $S$ up…

The objective of this article is to study nearly invariant subspaces of the backward shift operator on the real Hardy space. We also investigate nearly invariant subspaces with finite defect, and as a consequence, provide a characterization…

Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with…

In this paper, we establish the quasi-compactness of the transfer operator associated with skew product systems that are semi-conjugate to piecewise convex maps with a countably infinite number of branches. These non-invertible skew…

Determinantal point processes (DPPs) are repulsive point processes where the interaction between points depends on the determinant of a positive-semi definite matrix. The contributions of this paper are two-fold. First of all, we introduce…

We study Palm measures of determinantal point processes with $J$-Hermitian correlation kernels. A point process $\mathbb{P}$ on the punctured real line $\mathbb{R}^* = \mathbb{R}_{+} \sqcup \mathbb{R}_{-}$ is said to be $\textit{balanced…