Related papers: Self-affine sponges with random contractions

We show that an $n$-dimensional surface whose entropy is close to that of an $n$-dimensional plane is close in Hausdorff distance to some $n$-dimensional plane at every scale. Moreover we show that self-expanders of low entropy converge in…

We introduce the discrete affine group of a regular tree as a finitely generated subgroup of the affine group. We describe the Poisson boundary of random walks on it as a space of configurations. We compute isoperimetric profile and Hilbert…

We consider a class of random banded Hessenberg matrices with independent entries having identical distributions along diagonals. The distributions may be different for entries belonging to different diagonals. For a sequence of $n\times n$…

We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to…

We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…

Let $ K $ be a compact subset of the $d$-torus invariant under an expanding diagonal endomorphism with $ s $ distinct eigenvalues. Suppose the symbolic coding of $K$ satisfies weak specification. When $ s \leq 2 $, we prove that the…

This paper studies a large class of continuous functions $f:[0,1]\to\mathbb{R}^d$ whose range is the attractor of an iterated function system $\{S_1,\dots,S_{m}\}$ consisting of similitudes. This class includes such classical examples as…

We are interested in abstract conditions that characterize homomorphic images of affine quandles. Our main result is a two-fold characterization of this class: one by a property of the displacement group, the other one by a property of the…

In semialgebraic geometry, projections play a prominent role. A definable choice is a semialgebraic selection of one point in every fiber of a projection. Definable choices exist by semialgebraic triviality, but their complexity depends…

We investigate the semigroup of integer points inside a convex cone. We extend classical results in integer linear programming to integer conic programming. We show that the semigroup associated with nonpolyhedral cones can sometimes have a…

We determine the Hausdorff dimension for the range of a class of pure jump Markov processes in $\mathbb{R}^d$, which turns out to be random and depends on the trajectories of these processes. The key argument is carried out through the SDE…

In our recent work we described conditions under which a multi-parameter random simplicial complex is connected and simply connected. We showed that the Betti numbers of multi-parameter random simplicial complexes in one specific dimension…

For every proper convex cone $K \subset \mathbb R^3$ there exists a unique complete hyperbolic affine 2-sphere with mean curvature $-1$ which is asymptotic to the boundary of the cone. Two cones are associated if the corresponding affine…

We use obstruction theory based on the unstable Adams spectral sequence to construct self maps of finite quaternionic projective spaces. As a result, a conjecture of Feder and Gitler regarding the classification of self maps up to homology…

We introduce a simple, general, and convergent scheme to compute generalized eigenfunctions of self-adjoint operators with continuous spectra on rigged Hilbert spaces. Our approach does not require prior knowledge about the eigenfunctions,…

Consider a finite sequence of independent random permutations, chosen uniformly either among all permutations or among all matchings on n points. We show that, in probability, as n goes to infinity, these permutations viewed as operators on…

In this paper, we study the existence of the random approximations and fixed points for random almost lower semicontinuous operators defined on finite dimensional Banach spaces, which in addition, are condensing or 1-set-contractive. Our…

We show that the distribution of self-normalized sums of free self-adjoint random variables converges weakly to Wigner's semicircle law under appropriate conditions and estimate the rate of convergence in terms of the Kolmogorov distance.…

Let $C\subset\mathbb{N}^p$ be an integer polyhedral cone. An affine semigroup $S\subset C$ is a $ C$-semigroup if $| C\setminus S|<+\infty$. This structure has always been studied using a monomial order. The main issue is that the choice of…

A random spherical polytope $P_n$ in a spherically convex set $K \subset S^d$ as considered here is the spherical convex hull of $n$ independent, uniformly distributed random points in $K$. The behaviour of $P_n$ for a spherically convex…