Related papers: One-dimensional general forest fire processes

Cascades on random networks are typically analyzed by assuming they map onto percolation processes and then are solved using generating function formulations. This approach assumes that the network is infinite and weakly connected, yet…

We consider the process of uncovering the vertices of a random labeled tree according to their labels. First, a labeled tree with $n$ vertices is generated uniformly at random. Thereafter, the vertices are uncovered one by one, in order of…

We consider large uniform random trees where we fix for each vertex its degree and height. We prove, under natural conditions of convergence for the profile, that those trees properly renormalized converge. To this end, we study the paths…

The properties of randomly evolving special trees having defined and analyzed already in two earlier papers (arXiv:cond-mat/0205650 and arXiv:cond-mat/0211092) have been investigated in the case when the continuous time parameter converges…

The contact process is a simple model for the spread of an infection in a structured population. We investigate the case when the underlying structure evolves dynamically as a degree-dependent dynamical percolation model. Starting with a…

The diameter distribution of a given species of deciduous trees in mature, temperate zone forests is well approximated by a Gamma distribution. Here we give new experimental evidence for this conjecture by analyzing deciduous tree size data…

We propose generalized random forests, a method for non-parametric statistical estimation based on random forests (Breiman, 2001) that can be used to fit any quantity of interest identified as the solution to a set of local moment…

Regression models for supervised learning problems with a continuous target are commonly understood as models for the conditional mean of the target given predictors. This notion is simple and therefore appealing for interpretation and…

We present a coalescent process where three particles merge at each coagulation step. Using a random walk representation, we prove duality with a fragmentation process, whose fragmentation law we specify explicitly. Furthermore, we give a…

The forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…

The objective of the present study is twofold. First, the last developments and validation results of a hybrid model designed to simulate fire patterns in heterogeneous landscapes are presented. The model combines the features of a…

Increasing wildfire occurrence has spurred growing interest in wildfire spread prediction. However, even the most complex wildfire models diverge from observed progression during multi-day simulations, motivating need for data assimilation.…

The role of forest heterogeneity in the long-term, large-scale dynamics of forest fires is investigated by means of a cellular automata model and mean field approximation. Heterogeneity was conceived as trees (or acres of forest) with…

We develop a theory of insertion and deletion tolerance for point processes. A process is insertion-tolerant if adding a suitably chosen random point results in a point process that is absolutely continuous in law with respect to the…

In this paper we are concerned with bias voter models on trees and lattices, where the vertex in state 0 reconsiders its opinion at a larger rate than that of the vertex in state 1. For the process on tree with product measure as initial…

Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…

We consider a model of random tree growth, where at each time unit a new vertex is added and attached to an already existing vertex chosen at random. The probability with which a vertex with degree $k$ is chosen is proportional to $w(k)$,…

Machine learning models deployed in real-world settings must operate under evolving data distributions and constrained computational resources. This challenge is particularly acute in non-stationary domains such as energy time series,…

The dynamic problem of enclosing an expanding fire can be modelled by a discrete variant in a grid graph. While the fire expands to all neighbouring cells in any time step, the fire fighter is allowed to block $c$ cells in the average…

We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…