相关论文: Rigidity of the $\operatorname{Sine}_{\beta}$ proc…

Bessel processes associated with the root systems $A_{N-1}$ and $B_N$ describe interacting particle systems with $N$ particles on $\mathbb R$; they form dynamic versions of the classical $\beta$-Hermite and Laguerre ensembles. In this paper…

We characterize the (essentially) decreasing sequences of positive numbers $\beta$ = ($\beta$ n) for which all composition operators on H 2 ($\beta$) are bounded, where H 2 ($\beta$) is the space of analytic functions f in the unit disk…

In this paper, we study the Martin kernels of general open sets associated with inaccessible points for a large class of purely discontinuous Feller processes in metric measure spaces. Let $D$ be an unbounded open set. Infinity is…

We find the precise rate at which the empirical measure associated to a $\beta$-ensemble converges to its limiting measure. In our setting the $\beta$-ensemble is a random point process on a compact complex manifolds distributed according…

The {\it number rigidity} of a stationary point process $\mathsf{P}$ entails that for a bounded set $A$ the knowledge of $\mathsf{P}$ on $A^{c}$ a.s. determines $\mathsf{P}(A)$; the $k$-order rigidity means the moments of $\mathsf{P}1_{A}$…

This note reports the following observation: the finite-volume expectation value of the spin operator (the one-point function) between the $\mathbb{Z}_2$-even and odd ground states in the critical periodic Ising chain, when continued as a…

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…

We give a complete characterization of the sequences $\beta = (\beta_n)$ of positive numbers for which all composition operators on $H^2 (\beta)$ are bounded, where $H^2 (\beta)$ is the space of analytic functions $f$ on the unit disk…

In this paper we prove the uniqueness of the critical point for stable solutions of the Robin problem \[ \begin{cases} -\Delta u=f(u)&\text{in }\Omega\\ u>0&\text{in }\Omega\\ \partial_\nu u+\beta u=0&\text{on }\partial\Omega, \end{cases}…

In this note we study a natural measure on plane partitions giving rise to a certain discrete-time Muttalib-Borodin process (MBP): each time-slice is a discrete version of a Muttalib-Borodin ensemble (MBE). The process is determinantal with…

It is well known that the edge limit of Gaussian/Laguerre Beta-ensembles, as well as a large class of $\beta$-ensembles is given by the $\mathrm{Airy}(\beta)$ point process. We extend this universality result to a general class of additions…

A H"older regularity index at given points for density states of (alpha,1,beta)-superprocesses with alpha>1+beta is determined. It is shown that this index is strictly greater than the optimal index of local H"older continuity for those…

Let $A$ be abelian variety over the function field $K$ of a compact Riemann surface $B$. Fix a model $f \colon \mathcal{A} \to B$ of $A/K$ and a certain effective horizontal divisor $\DD \subset \mathcal{A}$. We give a sufficient condition…

We use discrete analogs of Riemann-Hilbert problem's methods to derive the discrete Bessel kernel which describes the poissonized Plancherel measures for symmetric groups. To do this we define discrete analogs of a Riemann-Hilbert problem…

Let $K$ be a number field, $S$ a finite set of places. For $\mathbb{G}_m$ or an elliptic curve $E$ defined over $K$, we establish uniformity results on the number of $S$-integral torsion points relative to a non-torsion point $\beta$, as…

A 2-dimensional point-line framework is a collection of points and lines in the plane which are linked by pairwise constraints that fix some angles between pairs of lines and also some point-line and point-point distances. It is rigid if…

We study orthogonal polynomial ensembles whose weights are deformations of exponential weights, in the limit of a large number of particles. The deformation symbols we consider affect local fluctuations of the ensemble around a bulk point…

We consider the interacting Bessel processes, a family of multiple-particle systems in one dimension where particles evolve as individual Bessel processes and repel each other via a log-potential. We consider two limiting regimes for this…

Let $X_t$ be any additive process in $\mathbb{R}^d.$ There are finite indices $\delta_i, \beta_i, i=1,2$ and a function $u$, all of which are defined in terms of the characteristics of $X_t$, such that \liminf_{t\to0}u(t)^{-1/\eta}X_t^*=…

The main result of this paper is that almost every realization of the sine-process with one particle removed is a uniqueness set for the Paley-Wiener space; with two particles removed, a zero set for the Paley-Wiener space.