Related papers: One-dimensional general forest fire processes

We consider the so-called one-dimensional forest fire process. At each site of $\mathbb{Z}$, a tree appears at rate $1$. At each site of $\mathbb{Z}$, a fire starts at rate ${\lambda}>0$, immediately destroying the whole corresponding…

Consider the following forest-fire model on the upper half-plane of the triangular lattice: Each site can be "vacant" or "occupied by a tree". At time 0 all sites are vacant. Then the process is governed by the following random dynamics:…

Consider the following forest fire model where the possible locations of trees are the sites of $\mathbb{Z}$. Each site has three possible states: 'vacant', 'occupied' or 'burning'. Vacant sites become occupied at rate $1$. At each site,…

We study the local limit of the fixed-point forest, a tree structure associated to a simple sorting algorithm on permutations. This local limit can be viewed as an infinite random tree that can be constructed from a Poisson point process…

We study the long-time dynamics of a forest-fire model with deterministic tree growth and instantaneous burning of entire forests by stochastic lightning strikes. Asymptotically the system organizes into a coarsening self-similar mosaic of…

We consider random dynamics on a uniform random recursive tree with $n$ vertices. Successively, in a uniform random order, each edge is either set on fire with some probability $p_n$ or fireproof with probability $1-p_n$. Fires propagate in…

We present a general stochastic forest-fire model which shows a variety of different structures depending on the parameter values. The model contains three possible states per site (tree, burning tree, empty site) and three parameters (tree…

We study generalizations of the Forest Fire model introduced in [van den Berg, J., and J\'arai, A. A. "On the asymptotic density in a one-dimensional self-organized critical forest-fire model". Comm. Math. Phys. 253 (2005)] and [Volkov,…

Habitat loss is one of the biggest threats facing plant species nowadays. We formulate a simple mathematical model of seed dispersal on reduced habitats to discuss survival of the species in relation to the habitat size and seeds production…

Consider the following forest-fire process on a connected graph. Each site of the graph can be either occupied or vacant. A vacant site becomes occupied with rate 1. A site is ignited with rate lambda, and its whole occupied cluster burns…

Place one active particle at the root of a graph and a Poisson-distributed number of dormant particles at the other vertices. Active particles perform simple random walk. Once the number of visits to a site reaches a random threshold, any…

We define some new sequences of recursively constructed random combinatorial trees, and show that, after properly rescaling graph distance and equipping the trees with the uniform measure on vertices, each sequence converges almost surely…

Consider the following partial "sorting algorithm" on permutations: take the first entry of the permutation in one-line notation and insert it into the position of its own value. Continue until the first entry is 1. This process imposes a…

We consider a generalization of the forest fire model on $\mathbb{Z}_+$ with ignition at zero only, studied in [arXiv:0907.1821]. Unlike that model, we allow delays in the spread of the fires as well as the non-zero burning time of…

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…

We consider a class of reinforcement processes, called WARMs, on tree graphs. These processes involve a parameter $\alpha$ which governs the strength of the reinforcement, and a collection of Poisson processes indexed by the vertices of the…

Dynamic mean field theory is applied to the problem of forest fires. The starting point is the Monte Carlo simulation in a lattice of million cells. The statistics of the clusters is obtained by means of the Hoshen--Kopelman algorithm. We…

Forest fire spreading is a complex phenomenon characterized by a stochastic behavior. Nowadays, the enormous quantity of georeferenced data and the availability of powerful techniques for their analysis can provide a very careful picture of…

This paper presents the development of a new continuous forest fire model implemented as a weighted local small-world network approach. This new approach was designed to simulate fire patterns in real, heterogeneous landscapes. The wildland…

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…