Related papers: Self-similar random structures defined as fixed po…

Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…

We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use…

Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of…

This work is a comparative study between the existence of fixed point for homomorphisms in a class of binary relationnal systems and the existence of fixed point for nonexpansive mappings in semimetric spaces.

In the context of tvs-cone metric spaces, we prove a Bishop-Phelps and a Caristi's type theorem. These results allow us to prove a fixed point theorem for $(\delta, L)$-weak contraction according to a pseudo Hausdorff metric defined by…

We consider a random walk on a multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death. We introduce an auxiliary "core" process that has a regenerative…

Associated to any finite metric space are a large number of objects and quantities which provide some degree of structural or geometric information about the space. In this paper we show that in the setting of subsets of weighted Hamming…

We develop the complex-analytic viewpoint on the tree convolutions studied by the second author and Weihua Liu in "An operad of non-commutative independences defined by trees" (Dissertationes Mathematicae, 2020, doi:10.4064/dm797-6-2020),…

We provide a uniform approach to obtain sufficient criteria for a (higher order) fixed point of a given bracket structure on a manifold to be stable under deformations. Examples of bracket structures include Lie algebroids, Lie…

We consider linear dynamical systems under floating-point rounding. In these systems, a matrix is repeatedly applied to a vector, but the numbers are rounded into floating-point representation after each step (i.e., stored as a…

Selecting N random points in a unit square corresponds to selecting a random permutation. By putting 5 types of symmetry restrictions on the points, we obtain subsets of permutations : involutions, signed permutations and signed…

This paper deals with the problem of detecting non-isotropic high-dimensional geometric structure in random graphs. Namely, we study a model of a random geometric graph in which vertices correspond to points generated randomly and…

For a hyperbolic map f on a saddle type fractal Lambda with self-intersections, the number of f- preimages of a point x in Lambda may depend on x. This makes estimates of the stable dimensions more difficult than for diffeomorphisms or for…

We consider a recursively defined random set of points and its barycenter, where the random set is constructed by the following inductive rule: Given a realization of $n-1$ points, one of them is picked at random and serves as a source the…

Multidimensional record patterns are random sets of lattice points defined by means of a recursive stochastic construction. The patterns thus generated owe their richness to the fact that the construction is not based on a total order,…

Random code-trees with necks were introduced recently to generalise the notion of $V$-variable and random homogeneous sets. While it is known that the Hausdorff and packing dimensions coincide irrespective of overlaps, their exact Hausdorff…

A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…

On a complete, connected, locally compact, non-compact geodesic space $(X,d)$, we assign each compact set a distance-like function. With the help of these functions, we obtain a pseudo-metric on the space of (non-empty) compact subsets of…

We consider finite point subsets (distributions) in compact metric spaces. Non-trivial bounds for sums of distances between points of distributions and for discrepancies of distributions in metric balls are given in the case of general…

The problem of comparing probability distributions is at the heart of many tasks in statistics and machine learning. Established comparison methods treat the standard setting that the distributions are supported in the same space. Recently,…