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

Let $\Gamma$ be a Zariski dense convex cocompact subgroup contained in an arithmetic lattice of $\operatorname{SO}(n, 1)^{\circ}$. We prove uniform exponential mixing of the geodesic flow for congruence covers of the hyperbolic manifold…

Regional frequency analysis is an important tool to properly estimate hydrological characteristics at ungauged or partially gauged sites in order to prevent hydrological disasters. The delineation of homogeneous groups of sites is an…

The method of moments is a classical statistical technique for density estimation that solves a system of moment equations to estimate the parameters of an unknown distribution. A fundamental question critical to understanding…

For a simply connected complex algebraic variey $X$, by the mixed Hodge structures $(W_{\bullet}, F^{\bullet})$ and $(\tilde W_{\bullet}, \tilde F^{\bullet})$ of the homology group $H_{*}(X;\mathbb Q)$ and the homotopy groups…

We consider the questions of efficient mixing and un-mixing by incompressible flows which satisfy periodic, no-flow, or no-slip boundary conditions on a square. Under the uniform-in-time constraint $\|\nabla u(\cdot,t)\|_p\leq 1$ we show…

The paper presents methods of eigenvalue localisation of regular matrix polynomials, in particular, stability of matrix polynomials is investigated. For this aim a stronger notion of hyperstability is introduced and widely discussed. Matrix…

The $\mu$-$\tau$ reflection symmetry $(\nu_{e},\thinspace\nu_{\mu},\thinspace\nu_{\tau})\rightarrow(\overline{\nu}_{e},\thinspace\overline{\nu}_{\tau},\thinspace\overline{\nu}_{\mu})$ and the TM1 mixing (a PMNS matrix with the first column…

We prove that every probability measure $\mu$ satisfying the stationary Fokker-Planck-Kolmogorov equation obtained by a $\mu$-integrable perturbation $v$ of the drift term $-x$ of the Ornstein-Uhlenbeck operator is absolutely continuous…

We consider the advection equation on $\mathbb{T}^2$ with a real analytic and time-periodic velocity field that alternates between two Hamiltonian shears. Randomness is injected by alternating the vector field randomly in time between just…

The polarization measure is the probability that among 3 individuals chosen at random from a finite population exactly 2 come from the same class. This index is maximum at the midpoints of the edges of the probability simplex. We compute…

Denoising diffusions sample from a probability distribution $\mu$ in $\mathbb{R}^d$ by constructing a stochastic process $({\hat{\boldsymbol x}}_t:t\ge 0)$ in $\mathbb{R}^d$ such that ${\hat{\boldsymbol x}}_0$ is easy to sample, but the…

This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution. First, we provide efficient algorithms for i.i.d. sampling,…

We propose a formally valid machine-learning-assisted global proposal mechanism for Monte Carlo sampling in lattice gauge theory. The construction is based on a coupling-flow update on the SU(2) lattice-link manifold, in which active links…

For any (Hausdorff) compact group $G$ with the normalized Haar measure ${\mathbf m}_G$, denote by ${\rm cp}(G)$ the probability ${\mathbf m}_{G\times G}(\{(x,y)\in G\times G \;|\; xy=yx\})$ of commuting a randomly chosen pair of elements of…

This work investigates a fully discrete mixed finite element method for the stochastic Boussinesq system driven by multiplicative noise. The spatial discretization is performed using a standard mixed finite element method, while the…

Let a sequence $(P_n)$ of polynomials in one complex variable satisfy a recurre ce relation with length growing slowlier than linearly. It is shown that $(P_n) $ is an orthonormal basis in $L^2_{\mu}$ for some measure $\mu$ on $\C$, if and…

Let $G$ be $\text{SO}^\circ(n,1)$ for $n \geq 3$ and consider a lattice $\Gamma < G$. Given a standard Borel probability $\Gamma$-space $(\Omega,\mu)$, consider a measurable cocycle $\sigma:\Gamma \times \Omega \rightarrow…

In this paper, we suggest a new heterogeneous multiscale method (HMM) for the time-harmonic Maxwell equations in locally periodic media. The method is constructed by using a divergence-regularization in one of the cell problems. This allows…

Let $(X, \mathcal{B}, \mu)$ be a probability measure space and $T_1$, $T_2$, $T_3$ three not necessarily commuting measure preserving transformations on $(X, \mathcal{B}, \mu)$. We prove that for all bounded functions $f_1$, $f_2$, $f_3$…

Persistent homology, the study of holes that appear in data as one thickens balls centered around its points over time, has theoretically guaranteed stability. That is, small data perturbations guarantee small changes in the lifetimes of…