相关论文: A stroll along the gamma
Let $\a$ be a complex random variable with mean zero and bounded variance $\sigma^{2}$. Let $N_{n}$ be a random matrix of order $n$ with entries being i.i.d. copies of $\a$. Let $\lambda_{1}, ..., \lambda_{n}$ be the eigenvalues of…
Asymptotics of maximum likelihood estimation for $\alpha$-stable law are analytically investigated with a continuous parameterization. The consistency and asymptotic normality are shown on the interior of the whole parameter space. Although…
This paper defines a new transport metric over the space of non-negative measures. This metric interpolates between the quadratic Wasserstein and the Fisher-Rao metrics and generalizes optimal transport to measures with different masses. It…
We present a new path integral method to analyze stochastically perturbed ordinary differential equations with multiple time scales. The objective of this method is to derive from the original system a new stochastic differential equation…
Let ${\Gamma}_n$ be an $n\times n$ Haar-invariant orthogonal matrix. Let ${ Z}_n$ be the $p\times q$ upper-left submatrix of ${\Gamma}_n$ and ${G}_n$ be a $p\times q$ matrix whose $pq$ entries are independent standard normals, where $p$ and…
We introduce a theory of probability in $\lambda$-rings designed to efficiently describe random variables valued in multisets of complex numbers, varieties over a field, or other similar enriched settings. A key role is played by the…
We find the explicit expression for the equilibrium wealth distribution of the Directed Random Market process, recently introduced by Mart\'inez-Mart\'inez and L\'opez-Ruiz, which turns out to be a Gamma distribution with shape parameter…
The aim of the presented research is to give a rigorous mathematical approach to Feynman path integrals based on strong (pathwise) approximations based on simple random walks.
Combining ideas of Pham, Sah, Sawhney, and Simkin on spread perfect matchings in super-regular bipartite graphs with an algorithmic blow-up lemma, we prove a spread version of the blow-up lemma. Intuitively, this means that there exists a…
From a suitable integral representation of the Laplace transform of a positive semi-definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…
The recently developed bag-of-paths (BoP) framework consists in setting a Gibbs-Boltzmann distribution on all feasible paths of a graph. This probability distribution favors short paths over long ones, with a free parameter (the temperature…
We investigate stochastic interpolation, a recently introduced framework for high dimensional sampling which bears many similarities to diffusion modeling. Stochastic interpolation generates a data sample by first randomly initializing a…
Using spectral embedding based on the signless Laplacian, we obtain bounds on the spectrum of transition matrices on graphs. As a consequence, we bound return probabilities and the uniform mixing time of simple random walk on graphs. In…
Partial identification often arises when the joint distribution of the data is known only up to its marginals. We consider the corresponding partially identified GMM model and develop a methodology for identification, estimation, and…
We study the geometry of probability distributions with respect to a generalized family of Csisz\'ar $f$-divergences. A member of this family is the relative $\alpha$-entropy which is also a R\'enyi analog of relative entropy in information…
We show that the mathematical form of the information measure of Fisher's I for a Gibbs' canonical probability distribution (the most important one in statistical mechanics) incorporates important features of the intrinsic structure of…
We present theoretical calculations of the ensemble-averaged (a.k.a. effective or coherent) wavefield propagating in a heterogeneous medium considered as one realization of a random process. In the literature, it is usually assumed that…
We formulate Bayesian updates in Markov processes by means of path integral techniques and derive the imaginary-time Schr\"{o}dinger equation with likelihood to direct the inference incorporated as a potential for the posterior probability…
This paper is concerned with determining the shortest path for a pursuer aiming to intercept a moving target travelling at a constant speed. To address this challenge, we introduce an efficient mathematical model outlined as an optimal…