Related papers: Radial rapid decay does not imply rapid decay

In this article we study a class of central extensions of $\mathbb{Z}\wr\mathbb{Z}$, as first described by Hall. On the one hand, we consider groups of this type with cyclic centre, our construction yields a rich class of groups. In…

It is known that gradient descent (GD) on a $C^2$ cost function generically avoids strict saddle points when using a small, constant step size. However, no such guarantee existed for GD with a line-search method. We provide one for a…

Let $A$ be a quasi-hereditary algebra. We prove that in many cases, a tilting module is rigid (i.e. has identical radical and socle series) if it does not have certain subquotients whose composition factors extend more than one layer in the…

Let $J$ be a semisimple Lie group with all simple factors of real rank at least two. Let $\Gamma<J$ be a lattice. We prove a very general local rigidity result about actions of $J$ or $\Gamma$. This shows that almost all so-called "standard…

We prove a noncommutative Bader-Shalom factor theorem for lattices with dense projections in product groups. As an application of this result and our previous works, we obtain a noncommutative Margulis factor theorem for all irreducible…

We analyze the convergence rate of the random reshuffling (RR) method, which is a randomized first-order incremental algorithm for minimizing a finite sum of convex component functions. RR proceeds in cycles, picking a uniformly random…

The random feature model exhibits a kind of resonance behavior when the number of parameters is close to the training sample size. This behavior is characterized by the appearance of large generalization gap, and is due to the occurrence of…

We reconsider the QCD predictions for the radiative decay $B\to \gamma \ell \nu_\ell$ with an energetic photon in the final state by taking into account the $1/E_\gamma, 1/m_b$ power-suppressed hard-collinear and soft corrections from…

The perturbative QCD corrections to the nonleptonic decay rate of the $b$ quark are discussed. By considering the limit where the final charmed quarks are slow, it is argued that the coefficients of the $\alpha_s^2$ terms, corresponding to…

In this paper we consider smoothness and decay properties of radial functions belonging to smoothness spaces related to Morrey spaces (Sobolev-Morrey spaces, Besov-type spaces and Besov-Morrey spaces). Within this framework we prove…

Let $\Gamma $ be an infinite discrete group and $\mathsf{A}\subset \Gamma $ a nonempty finite subset. The set of permutations $\sigma $ of $\Gamma $ such that $s^{-1}\sigma (s)\in \mathsf{A}$ for every $s\in \Gamma $ can be identified with…

In this paper we deal with a debonding model for a thin film in dimension two, where the wave equation on a time-dependent domain is coupled with a flow rule (Griffith's principle) for the evolution of the domain. We propose a general…

Let $\Gamma$ be the fundamental group of a compact n-dimensional riemannian manifold X of sectional curvature bounded above by -1. We suppose that $\Gamma$ is a free product of its subgroup A and B over the amalgamated subgroup C. We prove…

We study Riemannian manifolds $(M^n,g)$ with mean-convex boundary whose Ricci curvature is nonnegative in a spectral sense. Our first main result is a sharp spectral extension of a rigidity theorem by Kasue: we prove that under the…

We prove a result on approximate recovery, with high probability, of subgroups of a finite nonabelian group $\Gamma$ from their random perturbations. We use this for ad-hoc sequences of $\Gamma_n$ while passing to the continuum limit, in…

A group presentation is said to have rational growth if the generating series associated to its growth function represents a rational function. A long-standing open question asks whether the Heisenberg group has rational growth for all…

Let $\Gamma$ be a non-elementary Kleinian group and $H<\Gamma$ a finitely generated, proper subgroup. We prove that if $\Gamma$ has finite co-volume, then the profinite completions of $H$ and $\Gamma$ are not isomorphic. If $H$ has finite…

We study the decay law for a moving unstable particle. The usual time-dilatation formula states that the decay width for an unstable state moving with a momentum $p$ and mass $M$ is $\tilde{\Gamma}_{p}=\Gamma M/\sqrt{p^{2}+M^{2}}$ with…

Let $RG$ denote the group ring of the torsion group $G$ over a commutative ring $R$ with identity. In this paper we present proofs of some statements that appear without to be proved in the literature. We establish the valid implications…

It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform stability with respect to the family of unitary operators on…