Related papers: Asymptotics of maximum distance minimizers

We study various regularity properties of minimizers of the $\Phi$--perimeter, where $\Phi$ is a norm. Under suitable assumptions on $\Phi$ and on the dimension of the ambient space, we prove that the boundary of a cartesian minimizer is…

In this article, we study the maximal displacement in a branching random walk. We prove that its asymptotic behaviour consists in a first almost sure ballistic term, a negative logarithmic correction in probability and stochastically…

We show some results about the Hausdorff dimension of particular minimal but not uniquely ergodic interval exchange transformations. There is an appendix which shows that typical points for two different ergodic measures of an interval…

We show that the type function of a space with finite asymptotic dimension estimates its Hilbert (or any $l^p$) compression. The method allows to obtain the lower bound of the compression of the lamplighter group $Z\wr Z$, which has…

We calculate the long time and distance asymptotics of the one-particle correlation functions in the model of impenetrable spin 1/2 fermions in 1+1 dimensions. We consider the spin disordered zero temperature regime, which occurs when the…

We study a variant of the Falconer distance problem for dot products. In particular, for fractal subsets $A\subset \mathbb{R}^n$ and $a,x\in \mathbb{R}^n$, we study sets of the form \[ \Pi_x^a(A) := \{\alpha \in \mathbb{R} : (a-x)\cdot y=…

Performance accuracy of the Euclidean Distance Discriminant rule (EDDR) is studied in the high-dimensional asymptotic framework which allows the dimensionality to exceed sample size. Under mild assumptions on the traces of the covariance…

We study a variational problem modeling the behavior at equilibrium of charged liquid drops under convexity constraint. After proving well-posedness of the model, we show C 1,1-regularity of minimizers for the Coulombic interaction in…

In this paper, we are concerned with the existence and asymptotic behavior of minimizers for a minimization problem related to some quasilinear elliptic equations. Firstly, we proved that there exist minimizers when the exponent $q$ equals…

We study the properties of sets $\Sigma$ which are the solutions of the maximal distance minimizer problem, i.e. of sets having the minimal length (one-dimensional Hausdorff measure) over the class of closed connected sets $\Sigma \subset…

We examine the radial asymptotic behavior of spherically symmetric Lemaitre-Tolman-Bondi dust models by looking at their covariant scalars along radial rays, which are spacelike geodesics parametrized by proper length $\ell$, orthogonal to…

We are interested in the asymptotic behaviour of the first return time of the orbits of a dynamical system into a small neighbourhood of their starting points. We study this quantity in the context of dynamical systems preserving an…

We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence…

In this paper, we investigate the Hausdorff measure of shrinking target sets in $\beta$-dynamical systems. These sets are dynamically defined in analogy to the classical theory of weighted and multiplicative approximation. While the…

We consider the Dirichlet problem $-\Delta u=\lambda f(u)$ with $\lambda<0$ and $f$ non-negative and non-decreasing. We show existence and uniqueness of solutions $u_\lambda$ for any $\lambda$ and discuss their asymptotic behavior as…

The subject of this paper is a fragmentation equation with nonconservative solutions, some mass being lost to a dust of zero-mass particles as a consequence of an intensive splitting. Under some assumptions of regular variation on the…

Local asymptotic minimax risk bounds in a locally asymptotically mixture of normal family of distributions have been investigated under asymmetric loss functions and the asymptotic distribution of the optimal estimator that attains the…

We study a class of Landau-de Gennes energy functionals with a sextic bulk energy density in a three-dimensional domain. We examine the asymptotic behavior of uniformly bounded minimizers in two distinct scenarios: one where their energy…

Quasiperiodic systems offer an appealing intermediate between long-range ordered and genuine disordered systems, with unusual critical properties. One-dimensional models that break the so-called self-dual symmetry usually display a mobility…

I show that there exist minimal interval exchange transformations with an ergodic measure whose Hausdorff dimension is arbitrarily small, even 0. I will also show that in particular cases one can bound the Hausdorff dimension between $\frac…