Related papers: Expansion of Building-Like Complexes

We say that a metric graph is uniformly bounded if the degrees of all vertices are uniformly bounded and the lengths of edges are pinched between two positive constants; a metric space is approximable by a uniform graph if there is one…

We prove that a Poisson boundary of any regular thick Euclidean building, as well as lattices thereof is the space of chambers at infinity of the building with the harmonic measure class. We then use this result to generalize rigidity…

A $k$-configuration is a collection of $k$ distinct integers $x_1,\ldots,x_k$ together with their pairwise arithmetic means $\frac{x_i+x_j}{2}$ for $1 \leq i < j \leq k$. Building on recent work of Filmus, Hatami, Hosseini and Kelman on…

We give a full characterization of embeddings of the unit circle that admit a Sobolev homeomorphic extension to the unit disk. As a direct corollary, we establish that for quasiconvex target domains $\mathbb Y$, any homeomorphism $\varphi…

We prove that any proper, geodesic metric space whose Dehn function grows asymptotically like the Euclidean one has asymptotic cones which are non-positively curved in the sense of Alexandrov, thus are ${\rm CAT}(0)$. This is new already in…

We consider dynamical systems for which the spatial extension plays an important role. For these systems, the notions of attractor, epsilon-entropy and topological entropy per unit time and volume have been introduced previously. In this…

We prove that the crossing number of a graph decays in a continuous fashion in the following sense. For any epsilon>0 there is a delta>0 such that for a sufficiently large n, every graph G with n vertices and m > n^{1+epsilon} edges, has a…

Starting from a complete family (not defined by the reproducing kernel) for the unit sphere $\mathbf S^n$ in the complex $n$-space $\mathbb C^n$, we obtain an asymptotic expansion for the associated Berezin transform. The proof involves the…

We prove that given any positive integer $k$, for each open set $\Omega$ and any closed subset $D$ of its closure such that $\Omega$ is locally an (epsilon,delta)-domain near points in the boundary of $\Omega$ not contained in $D$ there…

Spatial structure can arise in spatial point process models via a range of mechanisms, including neighbour-dependent directionally biased movement. This spatial structure is neglected by mean-field models, but can have important effects on…

We obtain convergent inverse factorial expansions for the sum $S_n(a,b;c)$ of the first $n$ terms of the Gauss hypergeometric function of unit argument valid for $n\geq 1$. The form of these expansions depends on the location of the…

Asymptotic expansion is constructed and justified for the solution to a nonuniform Neumann boundary-value problem for the Poisson equation with the right-hand side that depends both on longitudinal and transversal variables in a thin…

Let G be a bounded simply connected domain and E be a regular compact subset of G with connected complement. We investigate the asymptotic behavior of the Kolmogorov k-width, k=k(n), of the set of polynomials of degree at most n having the…

It is proved that the projection constants of two- and three-dimensional spaces are bounded by $4/3$ and $(1+\sqrt 5)/2$, respectively. These bounds are attained precisely by the spaces whose unit balls are the regular hexagon and…

The quantum deformation $CP_q(N)$ of complex projective space is discussed. Many of the features present in the case of the quantum sphere can be extended. The differential and integral calculus is studied and $CP_q(N)$ appears as a quantum…

Let $n\geq 2$ and $1\leq q<p<\fz$. We prove that if $\Omega\subset\mathbb R^n$ is a Sobolev $(p, q)$-extension domain, with additional capacitory restrictions on boundary in the case $q\leq n-1$, $n>2$, then $|\partial\Omega|=0$. In the…

As the separation between galaxies increases owing to the expansion of the universe, galaxies themselves and smaller bound structures do not grow. An accurate description of the dynamics of cosmic structures requires the full apparatus of…

We develop a geometric approach to operator growth and Krylov complexity in many-body quantum systems governed by symmetries. We start by showing a direct link between a unitary evolution with the Liouvillian and the displacement operator…

The nonassociative generalization of supersymmetry is considered. It is shown that the associator of four supersymmetry generators has the coefficient $\sim \hbar/ \ell_0^2$ where $\ell_0$ is some characteristic length. Two cases are…

In this paper we study the global geometry of the Kobayashi metric on domains in complex Euclidean space. We are particularly interested in developing necessary and sufficient conditions for the Kobayashi metric to be Gromov hyperbolic. For…