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

The eigenvalues for the minors of real symmetric ($\beta=1$) and complex Hermitian ($\beta=2$) Wigner matrices form the Wigner corner process, which is a multilevel interlacing particle system. In this paper, we study the microscopic…

In Theorem 1 of the paper [V. Pata, A fixed point theorem in metric spaces, J. Fixed Point Theory Appl., 10 (2011), 299-305] it is proved that Picard's iterates for a function converge to a fixed point if a certain condition (C) is verified…

We prove that level $5$ Witten-Reshetikhin-Turaev $\mathrm{SO}(3)$ quantum representations, also known as the Fibonacci representations, of mapping class groups are locally rigid. More generally, for any prime level $\ell$, we prove that…

We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying…

Let L be a positive line bundle over a projective complex manifold X. Consider the space of holomorphic sections of the tensor power of order p of L. The determinant of a basis of this space, together with some given probability measure on…

In this paper we study a general family of multivariable Gaussian stochastic processes. Each process is prescribed by a fixed Borel measure $\sigma$ on $\mathbb R^n$. The case when $\sigma$ is assumed absolutely continuous with respect to…

We study the $O_\beta$-hull of a planar point set, a generalization of the Orthogonal Convex Hull where the coordinate axes form an angle $\beta$. Given a set $P$ of $n$ points in the plane, we show how to maintain the $O_\beta$-hull of $P$…

A critical point metric is a critical point of the total scalar curvature functional restricted to the space of constant scalar curvature metrics on a closed manifold with unit volume. It was conjectured in 1980's that every critical point…

We investigate the complexity of isomorphisms of computable structures on cones in the Turing degrees. We show that, on a cone, every structure has a strong degree of categoricity, and that degree of categoricity is $\bf{0^{(\alpha)}}$ for…

Infinite determinantal measures introduced in this note are inductive limits of determinantal measures on an exhausting family of subsets of the phase space. Alternatively, an infinite determinantal measure can be described as a product of…

We prove that curve complexes of surfaces are finitely rigid: for every orientable surface S of finite topological type, we identify a finite subcomplex X of the curve complex C(S) such that every locally injective simplicial map from X…

We investigate the hard edge scaling limit of the ensemble defined by the squared singular values of the product of two coupled complex random matrices. When taking the coupling parameter to be dependent on the size of the product matrix,…

We consider the hard-core model on a finite square grid graph with stochastic Glauber dynamics parametrized by the inverse temperature $\beta$. We investigate how the transition between its two maximum-occupancy configurations takes place…

The Bessel process with parameter $D>1$ and the Dyson model of interacting Brownian motions with coupling constant $\beta >0$ are extended to the processes in which the drift term and the interaction terms are given by the logarithmic…

Strongly anisotropic critical systems are considered in a $d$-dimensional film geometry. Such systems involve two (or more) distinct correlation lengths $\xi_\beta$ and $\xi_\alpha$ that scale as nontrivial powers of each other, i.e.\…

Determinantal point processes are point processes whose correlation functions are given by determinants of matrices. The entries of these matrices are given by one fixed function of two variables, which is called the kernel of the point…

A planar point set is in convex position precisely when it has a convex polygonization, that is, a polygonization with maximum interior angle measure at most \pi. We can thus talk about the convexity of a set of points in terms of the…

We define a finite Borel measure of Gibbs type, supported by the Sobolev spaces of negative indexes on the circle. The measure can be seen as a limit of finite dimensional measures. These finite dimensional measures are invariant by the…

Rice's Theorem states that every nontrivial language property of the recursively enumerable sets is undecidable. Borchert and Stephan initiated the search for complexity-theoretic analogs of Rice's Theorem. In particular, they proved that…

Bounded self-certification in Turing machines fails because self-simulation necessarily incurs a strictly positive temporal overhead. We translate this operational constraint into a domain-theoretic framework, defining an operator that…