Related papers: Polynomial 3-mixing for smooth time-changes of hor…

Let $(X,\mu)$ be a standard probability space. An automorphism $T$ of $(X,\mu)$ has the weak Pinsker property if for every $\varepsilon > 0$ it has a splitting into a direct product of a Bernoulli shift and an automorphism of entropy less…

This paper deals with random dynamical systems of polynomial automorphisms (complex generalized H\'{e}non maps and their conjugate maps) of $\Bbb{C}^{2}.$ We show that a generic random dynamical system of polynomial automorphisms has ``mean…

This work aims to investigate the well-posedness and the existence of ergodic invariant measures for a class of third grade fluid equations in bounded domain $D\subset\mathbb{R}^d,d=2,3,$ in the presence of a multiplicative noise. First, we…

The generation of 3D molecules requires simultaneously deciding the categorical features~(atom types) and continuous features~(atom coordinates). Deep generative models, especially Diffusion Models (DMs), have demonstrated effectiveness in…

We introduce a new broadly unifying family of combinatorial objects, which we call permutation flows, associated to an acyclic directed graph $G$ together with a framing $F$. This new family is combinatorially rich and contains as special…

We consider the global minimization of a polynomial on a compact set B. We show that each step of the Moment-SOS hierarchy has a nice and simple interpretation that complements the usual one. Namely, it computes coefficients of a polynomial…

This paper provides an estimate of the sum of a homogeneous polynomial $P$ of degree $\nu$ and mean zero over the lattice points inside a sphere of radius $R$. It is proved that $$ \sum_{\mathbf x \in \mathbb Z^3 \atop |\mathbf x| \le R}…

Let $\Gamma$ be a geometrically finite discrete subgroup in $\operatorname{SO}(d+1,1)^{\circ}$ with parabolic elements. We establish exponential mixing of the geodesic flow on the unit tangent bundle $\operatorname{T}^1(\Gamma\backslash…

Let $M$ be a closed oriented surface endowed with a Riemannian metric $g$ and let $\Omega$ be a 2-form. We show that the magnetic flow of the pair $(g,\Omega)$ has zero asymptotic Maslov index and zero Liouville action if and only $g$ has…

In this paper, we study entire solutions of the difference equation $\psi(z+h)=M(z)\psi(z)$, $z\in{\mathbb C}$, $\psi(z)\in {\mathbb C}^2$. In this equation, $h$ is a fixed positive parameter and $M: {\mathbb C}\to SL(2,{\mathbb C})$ is a…

We study the stochastic 3D primitive equations of the atmospheric mechanics. We consider them under a bounded and non-degenerate noise, which is statistically periodic in time with period $1$. In such a case we prove that the associated…

This note presents some equalities in law for $Z_N:=\det(\Id-G)$, where $G$ is an element of a subgroup of the set of unitary matrices of size $N$, endowed with its unique probability Haar measure. Indeed, under some general conditions,…

Let $(X,\mathcal{B},\mu)$ be a probability space and let $T_1,..., T_l$ be $l$ commuting invertible measure preserving transformations \linebreak of $X$. We show that if $T_1^{c_1} ... T_l^{c_l}$ is ergodic for each $(c_1,...,c_l)\neq…

Let H=A+UBU* where A and B are two N-by-N Hermitian matrices and U is a Haar-distributed random unitary matrix, and let \mu_H, \mu_A, and \mu_B be empirical measures of eigenvalues of matrices H, A, and B, respectively. Then, it is known…

We consider the problem of stable sampling of multivariate real polynomials of large degree in a general framework where the polynomials are defined on an affine real algebraic variety $M$, equipped with a weighted measure. In particular,…

We report on a computational parameter space study of mixing protocols for a half-full bi-axial spherical granular tumbler. The quality of mixing is quantified via the intensity of segregation (concentration variance) and computed as a…

We consider polynomials of the form $\operatorname{h}_m(y_1^{[\varkappa_1]},\ldots,y_n^{[\varkappa_n]})$, where $\operatorname{h}_m$ is the complete homogeneous polynomial of degree $m$ and $y_j^{[\varkappa_j]}$ denotes $y_j$ repeated…

A mixing flow with homogeneous spectrum of multiplicity 2 is presented.

In this paper, we study the stability of matrix polynomials under structured perturbations of their coefficients. More precisely, we consider a family of matrix polynomials \[…

In this article, it is proved that for any cumulative distribution function with compact support and a specified t > 0, there exists a diffusion martingale which has this law at time t. The article proves existence; no claims are made about…