相关论文: A concentration theorem for projections

We study spherical, charged and self--similar distributions of matter in the diffusion approximation. We propose a simple, dynamic but physically meaningful solution. For such a solution we obtain a model in which the distribution becomes…

Two-phase composites with non-overlapping inclusions randomly embedded in matrix are investigated. A straight forward approach is applied to estimate the effective properties of random 2D composites. First, deterministic boundary value…

Let $\Xi_n=\{\xi_1,\dots,\xi_n\}$ be a sample of $n$ independent points distributed in a regular closed element $K$ of the extended convex ring in $\mathbb{R}^d$ according to a probability measure $\mu$ on $K$, admitting a density function.…

Diffusion models have made rapid progress in generating high-quality samples across various domains. However, a theoretical understanding of the Lipschitz continuity and second momentum properties of the diffusion process is still lacking.…

Consider an nxn random matrix X with i.i.d. nonnegative entries with bounded density, mean m, and finite positive variance sigma^2. Let M be the nxn random Markov matrix with i.i.d. rows obtained from X by dividing each row of X by its sum.…

We investigate the weight distribution of random binary linear codes. For $0<\lambda<1$ and $n\to\infty$ pick uniformly at random $\lambda n$ vectors in $\mathbb{F}_2^n$ and let $C \le \mathbb{F}_2^n$ be the orthogonal complement of their…

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…

A previously found definition of complexity for spherically symmetric fluid distributions [1], is extended to axially symmetric static sources. In this case there are three different complexity factors, defined in terms of three structure…

While the mathematical foundations of score-based generative models are increasingly well understood for unconstrained Euclidean spaces, many practical applications involve data restricted to bounded domains. This paper provides a…

The properties of the square bias transformation are studied, in particular, the precise moment-type estimate for the $L_1$-metric between the transformed and the original distributions is proved, a relation between their characteristic…

We provide efficient algorithms for the problem of distribution learning from high-dimensional Gaussian data where in each sample, some of the variable values are missing. We suppose that the variables are missing not at random (MNAR). The…

We calculate finite-size effects of the Gaussian model in a L\times \tilde L^{d-1} box geometry with free boundary conditions in one direction and periodic boundary conditions in d-1 directions for 2<d<4. We also consider film geometry…

We consider the inverse problem for the polynomial map which sends an $m$-tuple of quadratic forms in $n$ variables to the sum of their $d$-th powers. This map captures the moment problem for mixtures of $m$ centered $n$-variate Gaussians.…

In this short note we prove a maximal concentration lemma for sub-Gaussian random variables stating that for independent sub-Gaussian random variables we have \[P<(\max_{1\le i\le N}S_{i}>\epsilon>)…

We study the higher-derivative equations for gauge potentials of arbitrary mixed-symmetry type obtained by setting to zero the divergences of the corresponding curvature tensors. We show that they propagate the same reducible multiplets as…

A class of discrete probability distributions contains distributions with limited support. A typical example is some variant of a Likert scale, with response mapped to either the $\{1, 2, \ldots, 5\}$ or $\{-3, -2, \ldots, 2, 3\}$ set. An…

We prove a formula for the evaluation of expectations containing a scalar function of a Gaussian random vector multiplied by a product of the random vector components, each one raised to a non-negative integer power. Some of the powers…

This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…

We study the total mass of high points in a random model for the Riemann-Zeta function. We consider the same model as in [8], [2], and build on the convergence to 'Gaussian' multiplicative chaos proved in [14]. We show that the total mass…

In this note we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an M-dimensional manifold of statistical…