Related papers: Restricted hypercontractivity on the Poisson space

Let $(X,d)$ be a complete, pathwise connected metric measure space with locally Ahlfors $Q$-regular measure $\mu$, where $Q>1$. Suppose that $(X,d,\mu)$ supports a (local) $(1,2)$-Poincar\'e inequality and a suitable curvature lower bound.…

Using normal family arguments, we show that the degree of the first nonzero homogenous polynomial in the expansion of $n$ dimensional Euclidean harmonic $K$-quasiconformal mapping around an internal point is odd, and that such a map from…

We consider solutions of the time-dependent Schr\"odinger equation for a potential localised at the points of a Poisson process. We prove convergence of the phase-space distribution in the annealed Boltzmann-Grad limit to a semiclassical…

\begin{abstract} We obtain sharp $L^p\rightarrow L^q$ hypercontractive inequalities for the weighted Bergman spaces on the unit disk $\mathbb{D}$ with the usual weights \\ $\frac{\alpha-1}{\pi}(1-|z|^2)^{\alpha-2},\alpha>1$ for $q\geq 2,$…

We prove $q$-super-Poincar\'e inequalities, $q \in [1, 2]$, for a class of exponential power type probability measures defined in terms of a norm in a number of subelliptic settings, primarily on stratified Lie groups but also in the…

We study compactness and boundedness of embeddings from Sobolev type spaces on metric spaces into $L^q$ spaces with respect to another measure. The considered Sobolev spaces can be of fractional order and some statements allow also…

We consider a conservative Markov semigroup on a semi-finite $W^*$-algebra. It is known that under some reasonable assumptions it is enough to determine a kind of differential structure on such a 'noncommutative space'. We construct an…

The Ornstein-Uhlenbeck process is interpreted as Brownian motion in a harmonic potential. This Gaussian Markov process has a bounded variance and admits a stationary probability distribution, in contrast to the standard Brownian motion. It…

We introduce a new collection of partially global Galois cohomology classes subsuming both plectic Heegner points and mock plectic invariants. The former are recovered as localizations of plectic Heegner classes, while the latter arise as…

In this article, we study the problem of parameter estimation for a discrete Ornstein - Uhlenbeck model driven by Poisson fractional noise. Based on random walk approximation for the noise, we study least squares and maximum likelihood…

A time inhomogeneous generalized Mehler semigroup on a real separable Hilbert space ${\mathds{H}}$ is defined through $$ p_{s,t}f(x)=\int_{\mathds{H}} f(U(t,s)x+y)\,\mu_{t,s}(dy), \quad t\geq s, \ x\in{\mathds{H}} $$ for every bounded…

Moser's Bernstein theorem \cite{moser61} says that an entire minimal graph of codimension 1 with bounded slope must be a hyperplane. An analogous result for arbitrary codimension is not true, by an example of Lawson-Osserman. Here, we show…

In another related work, U-statistics were used for non-asymptotic "average-case" analysis of random compressed sensing matrices. In this companion paper the same analytical tool is adopted differently - here we perform non-asymptotic…

Let $K$ be a non-polar compact subset of $\mathbb{R}$ and $\mu_K$ denote the equilibrium measure of $K$. Furthermore, let $P_n\left(\cdot, \mu_K\right)$ be the $n$-th monic orthogonal polynomial for $\mu_K$. It is shown that…

We establish the linear instability of the semiclassical Einstein-Klein-Gordon system linearised about the Minkowski vacuum spacetime. The proof relies on formulating a forcing problem for both metric and state perturbations within the…

We present a higher dimensional, scale-invariant version of a classical theorem of F. and M. Riesz. More precisely, we establish scale invariant absolute continuity of harmonic measure with respect to surface measure, along with higher…

We show that a random concave function having a periodic hessian on an equilateral lattice has a quadratic scaling limit, if the average hessian of the function satisfies certain conditions. We consider the set of all concave functions $g$…

In an attempt to develop higher-dimensional quasiconformal mappings on metric measure spaces with curvature conditions, i.e. from Ahlfors to Alexsandrov, we show that a non-collapsed $\mathrm{RCD}(0,n)$ space ($n\geq2$) with Euclidean…

We introduce the notion of Bartlett spectral measure for isometrically invariant random measures on proper metric commutative spaces. When the underlying Gelfand pair corresponds to a higher-rank, connected, simple matrix Lie group with…

We extend a global uniqueness result for the Calder\'on problem with partial data, due to Kenig-Sj\"ostrand-Uhlmann, to the case of less regular conductivities. Specifically, we show that in dimensions $n\ge 3$, the knowledge of the…