Related papers: Subgaussian 1-cocycles on discrete groups

Using Poincar\'e series of $ K $-finite matrix coefficients of integrable antiholomorphic discrete series representations of $ \mathrm{Sp}_{2n}(\mathbb R) $, we construct a spanning set for the space $ S_\rho(\Gamma) $ of Siegel cusp forms…

We show that, for a countable discrete group $\Gamma$, property $(\mathrm{T}_{L^p})$ of Bader, Furman, Gelander and Monod is equivalent to the property that, whenever an $L^p$-representation of $\Gamma$ admits a net of almost invariant unit…

Let $\pi$ traverse a sequence of cuspidal automorphic representations of GL(2) with large prime level, unramified central character and bounded infinity type. For G either of the groups GL(1) or PGL(2), let H(G) denote the assertion that…

The Bures metric and the associated Bures-Hall measure is arguably the best choice for studying the spectrum of the quantum mechanical density matrix with no apriori knowledge of the system. We investigate the probability of a gap in the…

Let $\Omega \subset \mathbb{R}^n$ be a convex. If $u: \Omega \rightarrow \mathbb{R}$ has mean 0, then we have the classical Poincar\'{e} inequality $$ \|u \|_{L^p} \leq c_p \mbox{diam}(\Omega) \| \nabla u \|_{L^p}$$ with sharp constants…

Recently, Schlage-Puchta proved super multiplicity of $p$-deficiency for normal subgroups of $p$-power index. We extend this result to all normal subgroups of finite index. We then use the methods of the proof to show that some groups with…

We prove that if a super-Poincar\'e inequality is satisfied by an infinitesimal generator $-A$ of a symmetric contracting semigroup then it implies a corresponding super-Poincar\'e inequality for $-g(A)$ with any Bernstein function $g$. We…

We study different notions of asymptotic growth for 1-cocycles of isometric representations on Banach spaces. One can see this as a way of quantifying the absence of fixed point properties on such spaces. Inspired by the work of Lafforgue,…

We show that the Poincar\'e lemma we proved elsewhere in the context of crystalline cohomology of higher level behaves well with regard to the Hodge filtration. This allows us to prove the Poincar\'e lemma for transversal crystals of level…

We refine the classical Cauchy--Schwartz inequality $\|X\|_{1} \leq \|X\|_{2}$ by demonstrating that for any $p$ and $q$ with $q>p>2$, there exists a constant $C=C(p,q)$ such that $\|X\|_1 \leq 1 - C \Big{(}\|X\|_p^p -…

We study the dynamics of the group of isometries of $L_p$-spaces. In particular, we study the canonical actions of these groups on the space of $\delta$-isometric embeddings of finite dimensional subspaces of $L_p(0,1)$ into itself, and we…

We show the $L^2$-Wasserstein contraction for the transition kernel of a discretised diffusion process, under a contractivity at infinity condition on the drift and a sufficiently high diffusivity requirement. This extends recent results…

We prove variation and oscillation $L^p$-inequalities associated with fractional derivatives of certain semigroups of operators and with the family of truncations of Riesz transforms in the inverse Gaussian setting. We also study these…

We give bounds on the Poincare (inverse spectral gap) constant of a non-negative, integer-valued random variable W, under negative dependence assumptions such as ultra log-concavity and total negative dependence. We show that the bounds…

This paper describes Clebsch-Gordan coefficients (CGCs) for unitary irreducible representations (UIRs) of the extended quantum mechanical Poincar\'e group $\pt$. `Extended' refers to the extension of the 10 parameter Lie group that is the…

We show that the categories of smooth ${\rm SL}_2({\mathbb Q}_p)$-representations (resp. ${\rm GL}_2({\mathbb Q}_p)$-representations) of level $1$ on $p$-torsion modules are equivalent with certain explicitly described equivariant…

We investigate discrete Poincar\'e inequalities on piecewise polynomial subspaces of the Sobolev spaces H(curl) and H(div) in three space dimensions. We characterize the dependence of the constants on the continuous-level constants, the…

We investigate the best constants for the regional fractional $p$-Poincar\'e inequality and the fractional $p$-Poincar\'e inequality in cylindrical domains. For the special case $p=2$, the result was already known due to…

The main results of this article concern the definition of a compactly supported cohomology class for the congruence group $\Gamma_0(p^n)$ with values in the second Milnor $K$-group (modulo 2-torsion) of the ring of $p$-integers of the…

We study first order differential operators with constant coefficients. The main question is under what conditions a generalized Poincar\'e inequality holds. We show that the constant rank condition is sufficient. The concept of the…