相关论文: Nontrivial Polydispersity Exponents in Aggregation…

We establish the universal edge scaling limit of random partitions with the infinite-parameter distribution called the Schur measure. We explore the asymptotic behavior of the wave function, which is a building block of the corresponding…

We discuss the propagation of scalars in a large class of non-extremal black hole and black p-brane geometries in generic dimensions. We show that the radial wave equation near the horizon possesses the SL(2,R) structure in every case;…

A recently proposed generalised continuum theory of curved dislocations describes the spatial and temporal evolution of statistically stored and geometrically necessary dislocation densities as well as the curvature. The dynamics follow…

We propose a new theoretical framework that exploits convolution kernels to transform a Volterra-type path-dependent (non-Markovian) stochastic process into a standard (Markovian) diffusion process. Remarkably, it is also possible to go…

In the present study we examine non-Gaussian spreading of solutes subject to advection, dispersion and kinetic sorption (adsorption/desorption). We start considering the behavior of a single particle and apply a random walk to describe…

The nonlinear diffusion equation $\frac{\partial \rho}{\partial t}=D \tilde{\Delta} \rho^\nu$ is analyzed here, where $\tilde{\Delta}\equiv \frac{1}{r^{d-1}}\frac{\partial}{\partial r} r^{d-1-\theta} \frac{\partial}{\partial r}$, and $d$,…

We calculate the spectral dimension of a wide class of tree-like fractals by solving the random walk problem through a new analytical technique, based on invariance under generalized cutting-decimation transformations. These fractals are…

Finding the mode of a high dimensional probability distribution $D$ is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when $D$ is…

In a recent string theory motivated paper, Nicolini, Smailagic and Spallucci (NSS) presented an interesting model for a noncommutative inspired, Schwarzschild-like black hole solution in 4-dimensions. The essential effect of having…

The modeling of coupled-channel effects has become increasingly important due to the availability of highly precise data for a large variety of hadronic (re)scattering processes. The K-matrix is a powerful, yet comparatively simple, method…

We study the problem of distributional approximations to high-dimensional non-degenerate $U$-statistics with random kernels of diverging orders. Infinite-order $U$-statistics (IOUS) are a useful tool for constructing simultaneous prediction…

We consider the defocusing nonlinear Schr{\"o}dinger equation with a gauge invariant power-like nonlinearity. We prove global dispersive estimates in a semi-classical scaling, after rescaling the solution thanks to a suitable distorsion of…

We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy ($\mathsf{KSD}$) and Wasserstein-2 metrics. Our key insight is that the time derivative of the…

A central challenge in Bayesian inference is efficiently approximating posterior distributions. Stein Variational Gradient Descent (SVGD) is a popular variational inference method which transports a set of particles to approximate a target…

In this paper, we derive rigorously a non-local cross-diffusion system from an interacting stochastic many-particle system in the whole space. The convergence is proved in the sense of probability by introducing an intermediate particle…

Kernel density estimation (KDE) is a popular statistical technique for estimating the underlying density distribution with minimal assumptions. Although they can be shown to achieve asymptotic estimation optimality for any input…

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…

The separated radial part of a sourceless massive complex scalar field equation on the Kerr-Newman black hole background is shown to be a generalized spin-weighted spheroidal wave equation of imaginary number order. While the separated…

In this article, using kernel convolution of order based dependent Dirichlet process (Griffin and Steel (2006)) we construct a nonstationary, nonseparable, nonparametric space-time process, which, as we show, satisfies desirable properties,…

We consider the mass-dependent aggregation process (k+1)X -> X, given a fixed number of unit mass particles in the initial state. One cluster is chosen proportional to its mass and is merged into one either with k-neighbors in one…