Related papers: Subgaussian 1-cocycles on discrete groups

Given a bounded subanalytic submanifold of $\mathbb{R}^n$, possibly admitting singularities within its closure, we study the cohomology of $L^p$ differential forms having an $L^p$ exterior differential (in the sense of currents) and…

Here we show existence of numerous subsets of Euclidean and metric spaces that, despite having empty interior, still support Poincar\'e inequalities. Most importantly, our methods do not depend on any rectilinear or self-similar structure…

We study stability of the sharp Poincar{\'e} constant of the invariant probability measure of a reversible diffusion process satisfying some natural conditions. The proof is based on the spectral interpretation of Poincar{\'e} inequalities…

We study the quantitative simplicity of the Lyapunov spectrum of $d$-dimensional bounded matrix cocycles subjected to additive random perturbations. In dimensions 2 and 3, we establish explicit lower bounds on the gaps between consecutive…

This article obtains purely metric counterparts of cornerstone results in the theory of embedding graphs into normed spaces. Our first main result is a metric analogue of Matou\v{s}ek's extrapolation relating the Poincar\'e constants…

We study unconditional subsequences of the canonical basis e_rc of elementary matrices in the Schatten class S^p. They form the matrix counterpart to Rudin's Lambda(p) sets of integers in Fourier analysis. In the case of p an even integer,…

We investigate properties of the Euler system associated to certain automorphic representations of the unitary similitude group GU(2,1) with respect to an imaginary quadratic field $E$, constructed by Loeffler-Skinner-Zerbes. By adapting…

We establish the existence of a spectral gap for the transfer operator induced on $\mathbb P^k = \mathbb P^k (\mathbb C)$ by a generic holomorphic endomorphism and a suitable continuous weight and its perturbations on various functional…

Suppose $\mathcal{G}$ is a second-countable locally compact Hausdorff \'{e}tale groupoid, $G$ is a discrete group containing a unital subsemigroup $P$, and $c:\mathcal{G}\rightarrow G$ is a continuous cocycle. We derive conditions on the…

We prove that there exists a martingale $f\in H_p $ such that the subsequence $\{L_{2^n}f \}$ of N\"orlund logarithmic means with respect to the Walsh system are not bounded in the Lebesgue space $weak-L_p $ for $0<p<1 $. Moreover, we prove…

Let $L$ denote a right-invariant sub-Laplacian on an exponential, hence solvable Lie group $G$, endowed with a left-invariant Haar measure. Depending on the structure of $G$, and possibly also that of $L$, $L$ may admit differentiable…

The classical $r$-matrix for $N=1$ superPoincar{\'e} algebra, given by Lukierski, Nowicki and Sobczyk is used to describe the graded Poisson structure on the $N=1$ Poincar{\'e} supergroup. The standard correspondence principle between the…

In this paper, we consider Wang's $CD_p(m,K)$ condition on graphs, which depends on the $p$-Laplacian $\Delta_p$ for $p>1$ and is an extension of the classical Bakry-\'Emery $CD(m,K)$ curvature dimension condition. We calculate several…

We consider generic properties of Lagrangians. Our main result is the Theorem of Kupka-Smale, in the Lagrangian setting, claiming that, for a convex and superlinear Lagrangian defined in a compact surface, for each $k\in \mathbb{R}$,…

We investigate the general class of second-order PDEs, invariant under the $d=1$ $\ell=\frac{1}{2}+{\mathbb N}_0$ centrally extended Conformal Galilei Algebras, pointing out that they are deformations of decoupled systems. For…

Many invariants of finitely generated positive cancelative commutative semigroups can be studied from their Poincar\'e series. We offer and present several closed formulas for them. Moreover, those formulas have elementary proofs and are…

We prove on some nested fractals scale invariant $L^p$-Poincar\'e inequalities on metric balls in the range $1 \le p \le 2$. Our proof is based on the development of the local $L^p$-theory of Korevaar-Schoen-Sobolev spaces on fractals using…

We study weighted Poincar\'e and Poincar\'e-Sobolev type inequalities with an explicit analysis on the dependence on the $A_p$ constants of the involved weights. We obtain inequalities of the form $$ \left…

Using the general theory of [10] ( hep-th 9412058 ), quantum Poincar\'e groups (without dilatations) are described and investigated. The description contains a set of numerical parameters which satisfy certain polynomial equations. For most…

We study the relation between the Galois group $G$ of a linear difference-differential system and two classes $\mathcal{C}_1$ and $\mathcal{C}_2$ of groups that are the Galois groups of the specializations of the linear difference equation…