Related papers: Asymptotics of one-dimensional forest fire process…

Let ${Z_{n},n\geq 0} $ be a critical branching process in random environment and let $T$ be its moment of extinction. Under the annealed approach we prove, as $n\to \infty ,$ a limit theorem for the number of particles in the process at…

We consider the contact process with infection rate $\lambda$ on a random $(d+1)$-regular graph with $n$ vertices, $G_n$. We study the extinction time $\tau_{G_n}$ (that is, the random amount of time until the infection disappears) as $n$…

On large scales, the Lyman-$\alpha$ forest provides insights into the expansion history of the Universe, while on small scales, it imposes strict constraints on the growth history, the nature of dark matter, and the sum of neutrino masses.…

Random forests are decision tree ensembles that can be used to solve a variety of machine learning problems. However, as the number of trees and their individual size can be large, their decision making process is often incomprehensible. In…

We study the statistical mechanics of a one-dimensional log gas with general potential and arbitrary beta, the inverse of temperature, according to the method we introduced for two-dimensional Coulomb gases in [SS2]. Such ensembles…

We study finite-size effects in the self-organized critical forest-fire model by numerically evaluating the tree density and the fire size distribution. The results show that this model does not display the finite-size scaling seen in…

We revisit the spatial ${\lambda}$-Fleming-Viot process introduced in [1]. Particularly, we are interested in the time $T_0$ to the most recent common ancestor for two lineages. We distinguish between the case where the process acts on the…

The explosive growth of spatial data and extensive utilization of spatial databases emphasize the necessity for the automated discovery of spatial knowledge. In modern times, spatial data mining has emerged as an area of voluminous…

Frozen percolation on the binary tree was introduced by Aldous around fifteen years ago, inspired by sol-gel transitions. We investigate a version of the model on the triangular lattice, where connected components stop growing ("freeze") as…

We study the scaling limit of random forest with prescribed degree sequence in the regime that the largest tree consists of all but a vanishing fraction of nodes. We give a description of the limit of the forest consisting of the small…

This thesis presents analysis of the properties and run-time of the Rapidly-exploring Random Tree (RRT) algorithm. It is shown that the time for the RRT with stepsize $\epsilon$ to grow close to every point in the $d$-dimensional unit cube…

Starting from any graph on $\{1, \ldots, n\}$, consider the Markov chain where at each time-step a uniformly chosen vertex is disconnected from all of its neighbors and reconnected to another uniformly chosen vertex. This Markov chain has a…

Given a graph, we can form a spanning forest by first sorting the edges in some order, and then only keep edges incident to a vertex which is not incident to any previous edge. The resulting forest is dependent on the ordering of the edges,…

The burning number is a recently introduced graph parameter indicating the spreading speed of content in a graph through its edges. While the conjectured upper bound on the necessary numbers of time steps until all vertices are reached is…

We examine the total number of collisions $C_n$ in the $\Lambda$-coalescent process which starts with $n$ particles. A linear growth and a stable limit law for $C_n$ are shown under the assumption of a power-like behaviour of the measure…

Random forests, introduced by Leo Breiman in 2001, are a very effective statistical method. The complex mechanism of the method makes theoretical analysis difficult. Therefore, a simplified version of random forests, called purely random…

Consider a standard ${\Lambda }$-coalescent that comes down from infinity. Such a coalescent starts from a configuration consisting of infinitely many blocks at time $0$, but its number of blocks $N_t$ is a finite random variable at each…

The probability that two randomly selected phylogenetic trees of the same size are isomorphic is found to be asymptotic to a decreasing exponential modulated by a polynomial factor. The number of symmetrical nodes in a random phylogenetic…

We present Neural Random Forest Imitation - a novel approach for transforming random forests into neural networks. Existing methods propose a direct mapping and produce very inefficient architectures. In this work, we introduce an imitation…

In this paper we prove a strong law of large numbers and its L^1-convergence counterpart for the process counted with a random characteristic in the context of self-similar fragmentation processes. This result extends a somewhat analogical…