相关论文: Local structure of random quadrangulations

We use a continued fraction approach to compare two statistical ensembles of quadrangulations with a boundary, both controlled by two parameters. In the first ensemble, the quadrangulations are bicolored and the parameters control their…

We propose a scheme for recycling Gaussian random vectors into structured matrices to approximate various kernel functions in sublinear time via random embeddings. Our framework includes the Fastfood construction as a special case, but also…

We give alternate constructions of (i) the scaling limit of the uniform connected graphs with given fixed surplus, and (ii) the continuum random unicellular map (CRUM) of a given genus that start with a suitably tilted Brownian continuum…

A construction as a growth process for sampling of the uniform infinite planar triangulation (UIPT), defined in a previous paper, is given. The construction is algorithmic in nature, and is an efficient method of sampling a portion of the…

We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…

We show in this paper that, when properly rescaled in time and in space, the characteristic polynomial of a random unitary matrix converges almost surely to a random analytic function whose zeros, which are on the real line, form a…

In this note we first consider local times of random walks killed at leaving positive half-axis. We prove that the distribution of the properly rescaled local time at point $N$ conditioned on being positive converges towards an exponential…

We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…

In this paper, we analyze the behavior of various non-parametric local regression estimators, i.e. estimators that are based on local averaging, for estimating a Lipschitz regression function at a fixed point, or in sup-norm. We first prove…

We introduce a notion of vague convergence for random marked metric measure spaces. Our main result shows that convergence of the moments of order $k \ge 1$ of a random marked metric measure space is sufficient to obtain its vague…

A class of discrete renewal processes with super-exponentially decaying inter-arrival distributions coincides with the infinite volume limit of general homogeneous pinning models in their localized phase. Pinning models are statistical…

Computational sampling has been central to the sciences since the mid-20th century. While machine-learning-based approaches have recently enabled major advances, their behavior remains poorly understood, with limited theoretical control…

We present a general method for the reconstruction of the one-point Probability Distribution Function of the local aperture mass in weak lensing maps. Exact results, that neglect the lens-lens coupling and departure form the Born…

We study two related probabilistic models of permutations and trees biased by their number of descents. Here, a descent in a permutation $\sigma$ is a pair of consecutive elements $\sigma(i), \sigma(i+1)$ such that $\sigma(i) >…

We develop inference procedures robust to general forms of weak dependence. The procedures utilize test statistics constructed by resampling in a manner that does not depend on the unknown correlation structure of the data. We prove that…

Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…

Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global…

Transforms using random matrices have been found to have many applications. We are concerned with the projection of a signal onto Gaussian-distributed random orthogonal bases. We also would like to easily invert the process through…

In this paper we propose a wide class of truncated stochastic approximation procedures with moving random bounds. While we believe that the proposed class of procedures will find its way to a wider range of applications, the main motivation…

The randomized Gauss--Seidel method and its extension have attracted much attention recently and their convergence rates have been considered extensively. However, the convergence rates are usually determined by upper bounds, which cannot…