Related papers: Depths in random recursive metric spaces

We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…

The rotor walk on a graph is a deterministic analogue of random walk. Each vertex is equipped with a rotor, which routes the walker to the neighbouring vertices in a fixed cyclic order on successive visits. We consider rotor walk on an…

We consider the Erdos-Renyi random graph G(n,p) inside the critical window, where p = 1/n + lambda * n^{-4/3} for some lambda in R. We proved in a previous paper (arXiv:0903.4730) that considering the connected components of G(n,p) as a…

The concept of trustworthy AI has gained widespread attention lately. One of the aspects relevant to trustworthy AI is robustness of ML models. In this study, we show how to probabilistically quantify robustness against naturally occurring…

In signal detection problems, one is usually faced with the task of searching a parameter space for peaks in the likelihood function which indicate the presence of a signal. Random searches have proven to be very efficient as well as easy…

We study the situations when the solution to a weighted stochastic recursion has a power law tail. To this end, we develop two complementary approaches, the first one extends Goldie's (1991) implicit renewal theorem to cover recursions on…

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,…

Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure is distinct from fixed weight updates. The probability for a…

The goal of these lectures is to survey some of the recent progress on the description of large-scale structure of random trees. We use the framework of Markov-Branching sequences of trees and discuss several applications.

Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…

In rank-metric cryptography, a vector from a finite dimensional linear space over a finite field is viewed as the linear space spanned by its entries. The rank decoding problem which is the analogue of the problem of decoding a random…

Margin-based learning, exemplified by linear and kernel methods, is one of the few classical settings where generalization guarantees are independent of the number of parameters. This makes it a central case study in modern highly…

In this paper, we embed metric space endowed with a convex combination operation, named convex combination space, into a Banach space and the embedding preserves the structures of metric and convex combination. For random element taking…

We study a generalisation of the random recursive tree (RRT) model and its multigraph counterpart, the uniform directed acyclic graph (DAG). Here, vertices are equipped with a random vertex-weight representing initial inhomogeneities in the…

There are numerous randomized algorithms to generate spanning trees in a given ambient graph; several target the uniform distribution on trees (UST), while in practice the fastest and most frequently used draw random weights on the edges…

We use the notions of reflexivity and of reflexive dimensions in order to introduce probability measures for lattice polytopes and initiate the investigation of their statistical properties. Examples of applications to discrete geometry…

While statistical learning methods have proved powerful tools for predictive modeling, the black-box nature of the models they produce can severely limit their interpretability and the ability to conduct formal inference. However, the…

This paper is a variation on the uniform spanning tree theme. We use random spanning forests to solve the following problem: for a Markov process on a finite set of size $n$, find a probability law on the subsets of any given size $m \leq…

We study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total…

We investigate the distribution of the depth of a node containing a specific key or, equivalently, the number of steps needed to retrieve an item stored in a randomly grown binary search tree. Using a representation in terms of mixed and…