Related papers: Bulk asymptotics for polyanalytic correlation kern…
We study the behaviors of the relative Bergman kernel metrics on holomorphic families of degenerating hyperelliptic Riemann surfaces and their Jacobian varieties. Near a node or cusp, we obtain precise asymptotic formulas with explicit…
Almost exponentially localized polynomial kernels are constructed on the unit ball $B^d$ in $\RR^d$ with weights %functions $W_\mu(x)= (1-|x|^2)^{\mu-1/2}$, $\mu \ge 0$, by smoothing out the coefficients of the corresponding orthogonal…
We consider sequences of biorthogonal polynomials with respect to a Cauchy type convolution kernel and give the weak and ratio asymptotic of the corresponding sequences of biorthogonal polynomials. The construction is intimately related…
In this paper we investigate the asymptotic behavior of polynomials that are orthonormal over the interior domain of an analytic Jordan curve L with respect to area measure. We prove that, inside L, these polynomials behave asymptotically…
Given a sequence of Hermitian holomorphic line bundles $(L_k,h_k)$ over a complex manifold $M$ which may not be compact, we generalize the scaling method in arXiv:2310.08048 to study the asymptotic behavior of the Bergman kernels and…
In this paper, we introduce the quaternionic slice polyanalytic functions and we prove some of their properties. Then, we apply the obtained results to begin the study of the quaternionic Fock and Bergman spaces in this new setting. In…
The eigenvalue correlations of random matrices from the Jacobi Unitary Ensemble have a known asymptotic behavior as their size tends to infinity. In the bulk of the spectrum the behavior is described in terms of the sine kernel, and at the…
We realize the Apollonian group associated to an integral Apollonian circle packings, and some of its generalizations, as a group of automorphisms of an algebraic surface. Borrowing some results in the theory of orbit counting, we study the…
The weak convergence of orthogonal polynomials is given under conditions on the asymptotic behaviour of the coefficients in the three-term recurrence relation. The results generalize known results and are applied to several systems of…
We consider linear approximation based on function evaluations in reproducing kernel Hilbert spaces of certain analytic weighted power series kernels and stationary kernels on the interval $[-1,1]$. Both classes contain the popular Gaussian…
We extend balloon and sample-smoothing estimators, two types of variable-bandwidth kernel density estimators, by a shift parameter and derive their asymptotic properties. Our approach facilitates the unified study of a wide range of density…
This paper complements the recent investigation of \cite{DM} on the asymptotic behavior of polynomials orthogonal over the interior of an analytic Jordan curve $L$. We study the specific case of $L=\{z= w-1 +(w-1)^{-1},\ |w|=R\}$, for some…
In this article, we consider the problem of estimating the heat kernel on measure-metric spaces equipped with a resistance form. Such spaces admit a corresponding resistance metric that reflects the conductivity properties of the set. In…
In this paper we compute the asymptotic behavior of the recurrence coefficients for polynomials orthogonal with respect to a logarithmic weight $w(x){\rm d}x = \log \frac{2k}{1-x}{\rm d}x$ on $(-1,1)$, $k > 1$, and verify a conjecture of…
We give a proof of universality in the bulk of spectrum of unitary matrix models, assuming that the potential is globally $C^{2}$ and locally $C^{3}$ function. The proof is based on the determinant formulas for correlation functions in…
We study the asymptotics of certain measures on partitions (the so-called z-measures and their relatives) in two different regimes: near the diagonal of the corresponding Young diagram and in the intermediate zone between the diagonal and…
We study the local statistics of orthogonal polynomial ensembles near a hard edge, subject to a multiplicative deformation of the measure. Probabilistically, this deformation corresponds to a position-dependent conditional thinning of the…
We consider the multi-point equal time height fluctuations of a one-dimensional polynuclear growth model in a half space. For special values of the nucleation rate at the origin, the multi-layer version of the model is reduced to a…
We consider asymptotics of planar orthogonal polynomials $P_{n,N}$ (where $\mathrm{deg}P_{n,N}=n$) with respect to the weight $$\frac{|z-w|^{2NQ_1}}{(1+|z|^2)^{N(1+Q_0+Q_1)+1}}, \quad(Q_0,Q_1 > 0)$$ in the whole complex plane. With $n,…
We prove that, for many parameterized problems in the class FPT, the existence of polynomial kernels implies the collapse of the W-hierarchy (i.e., W[P] = FPT). The collapsing results are also extended to assumed exponential kernels for…