Related papers: Volume distortion in groups

We show that the hyperplane conjecture holds for the classes of $k$-intersection bodies with arbitrary measures in place of volume.

We show that the two-point function of a quantum field theory with de Sitter momentum space (herein called DSR) can be expressed as the product of a standard delta function and an energy-dependent factor. This is a highly non-trivial…

At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…

We develop a theory for the representation of opaque solids as volumes. Starting from a stochastic representation of opaque solids as random indicator functions, we prove the conditions under which such solids can be modeled using…

Let $T_{k}$ be the expanding map of $[0,1)$ defined by $T_{k}(x) = k x\ \text{mod 1}$, where $k\geq 2$ is an integer. Given $0\leq a<b\leq 1$, let $\mathcal{W}_{k}(a,b)=\{x\in [0,1)\ \vert \ T_{k}^nx\notin (a,b), \text{ for all } n\geq 0\}$…

Symmetry breaking phase transitions are an example of non-equilibrium processes that require real time treatment, a major challenge in strongly coupled systems without long-lived quasiparticles. Holographic duality provides such an approach…

We establish new results on the dimensional properties of measures and invariant sets associated to random walks and group actions by circle diffeomorphisms. This leads to several dynamical applications. Among the applications, we show,…

Capacities of generalized condensers are applied to prove a two-point distortion theorem for conformal mappings. The result is expressed in terms of the Robin function and the Robin capacity with respect to the domain of definition of the…

The cross covariogram g_{K,L} of two convex sets K, L in R^n is the function which associates to each x in R^n the volume of the intersection of K with L+x. The problem of determining the sets from their covariogram is relevant in…

In this paper, we give a definition of volume for subsets in the space of arcs of an algebraic variety, and study its properties. Our main result relates the volume of a set of arcs on a Cohen-Macaulay variety to its jet-codimension, a…

Helly's theorem is a fundamental result in discrete geometry, describing the ways in which convex sets intersect with each other. If $S$ is a set of $n$ points in $R^d$, we say that $S$ is $(k,G)$-clusterable if it can be partitioned into…

In a previous work arXiv:physics/0611108v2, it was shown that the volume spanned by a molecular system in its conformational space can be effectively bounded by a polyhedral cone, this cone is described by means of a simple combinatorial…

We provide a formula to compute the volume of the intersection of a generalized cylinder with a hyperplane. Then we prove an integral inequality involving Bessel functions similar to Keith Ball's well-known inequality. Using this inequality…

Given a linear action of a group $G$ on a $K$-vector space $V$, we consider the invariant ring $K[V \oplus V^*]^G$, where $V^*$ is the dual space. We are particularly interested in the case where $V =\gfq^n$ and $G$ is the group $U_n$ of…

We use algebraic techniques to study homological filling functions of groups and their subgroups. If $G$ is a group admitting a finite $(n+1)$--dimensional $K(G,1)$ and $H \leq G$ is of type $F_{n+1}$, then the $n^{th}$--homological filling…

We discuss the relevance of Eisenstein series for representing certain G(Z)-invariant string theory amplitudes which receive corrections from BPS states only. The Eisenstein series are constructed using G(Z)-invariant mass formulae and are…

We present the first step towards the estimation of finite volume effects in heavy-light meson systems using heavy meson chiral perturbation theory. We demonstrate that these effects can be amplified in both light-quark and heavy-quark mass…

We give the sharp lower bound of the volume product of $n$-dimensional convex bodies which are invariant under a discrete subgroup $SO(K)=\{ g \in SO(n); g(K)=K \}$, where $K$ is an $n$-cube or $n$-simplex. This provides new partial results…

In this talk we discuss finite-volume computations of two-body hadronic decays below the inelastic threshold (e.g. $K\to\pi\pi$ decays). In particular we show how the relation between finite-volume matrix elements and physical amplitudes,…

A classical theorem of Jordan asserts that if a group $G$ acts transitively on a finite set of size at least $2$, then $G$ contains a derangement (a fixed-point free element). Generalisations of Jordan's theorem have been studied…