Related papers: Asymptotics of one-dimensional forest fire process…
We model the spatial dynamics of a forest stand by using a special class of spatio-temporal point processes, the sequential spatial point process, where the spatial dimension is parameterized and the time component is atomic. The sequential…
We consider additive functionals $X_n(\phi)$ with small toll functions on split trees and a generalization of split trees, which we call fractional split trees, where the split vector does not need to sum up to 1. These additive functionals…
Previous work indicates that tropical forest can exist as an alternative stable state to savanna. Therefore, perturbation by climate change or human impact may lead to crossing of a tipping point beyond which there is rapid forest dieback…
We investigate scaling limits of trees built by uniform attachment with freezing, which is a variant of the classical model of random recursive trees introduced in a companion paper. Here vertices are allowed to freeze, and arriving…
The basic object we consider is a certain model of continuum random tree, called the stable tree. We construct a fragmentation process $(F^-(t), t>=0)$ out of this tree by removing the vertices located under height $t$. Thanks to a…
Fire is an indissoluble component of ecosystems, however quantifying the effects of fire on vegetation is challenging task as fire lies outside the typical experimental design attributes. A recent simulation study showed that under…
We investigate the kinetics of systems in which particles of one species undergo binary fragmentation and pair annihilation. In the latter, nonlinear process, fragments react at collision to produce an inert species, causing loss of mass.…
Let $T$ be the extinction moment of a critical branching process $Z=(Z_{n},n\geq 0) $ in a random environment specified by iid probability generating functions. We study the asymptotic behavior of the probability of extinction of the…
We study a pure death process. At each discrete time every individual dies or not independently of each other with a constant probability. We give examples showing that in a certain limit extinction happens along a path where one and only…
We present a simple, efficient model for learning boundary detection based on a random forest classifier. Our approach combines (1) efficient clustering of training examples based on simple partitioning of the space of local edge…
In this paper, we study an exact solution of the asymmetric simple exclusion process on a periodic lattice of finite sites with two typical updates, i.e., random and parallel. Then, we find that the explicit formulas for the partition…
We consider the total cost of cutting down a random rooted tree chosen from a family of so-called very simple trees (which include ordered trees, $d$-ary trees, and Cayley trees); these form a subfamily of simply generated trees. At each…
We consider the spatial Lambda-Fleming-Viot process model for frequencies of genetic types in a population living in R^d, with two types of individuals (0 and 1) and natural selection favouring individuals of type 1. We first prove that the…
Forest fires may cause considerable damages both in ecosystems and lives. This proposal describes the application of Internet of Things and wireless sensor networks jointly with multi-hop routing through a real time and dynamic monitoring…
We consider a model of directed polymers on a regular tree with a disorder given by independent, identically distributed weights attached to the vertices. For suitable weight distributions this model undergoes a phase transition with…
We consider the contact process on finite and connected graphs and study the behavior of the extinction time, that is, the amount of time that it takes for the infection to disappear in the process started from full occupancy. We prove,…
Let $F(N,m)$ denote a random forest on a set of $N$ vertices, chosen uniformly from all forests with $m$ edges. Let $F(N,p)$ denote the forest obtained by conditioning the Erdos-Renyi graph $G(N,p)$ to be acyclic. We describe scaling limits…
In a multivariate nonparametric regression setting we construct explicit asymptotic uniform confidence bands for centered purely random forests. Since the most popular example in this class of random forests, namely the uniformly centered…
The increasing frequency and severity of wildfires highlight the need for accurate fire and plume spread models. We introduce an approach that effectively isolates and tracks fire and plume behavior across various spatial and temporal…
Consider a discrete-time process on a graph $G$ where a set $B$ of initial vertices are chosen to be colored blue (the remainder being white) and then a time step consists of every currently blue vertex forcing all of its neighbors to…