57 citations · 226 across the 15 of their papers we have counts for
19 papers
On the threshold of spread-out contact process percolation
Balazs Rath, Daniel Valesin
We study the stationary distribution of the (spread-out) -dimensional contact process from the point of view of site percolation. In this process, vertices of can…
Age evolution in the mean field forest fire model via multitype branching processes
Edward Crane, Balazs Rath, Dominic Yeo
We study the distribution of ages in the mean field forest fire model introduced by Ráth and Tóth. This model is an evolving random graph whose dynamics combine Erdős-Rényi edge-ad…
One-dimensional Multi-particle DLA -- a PDE approach
Vladas Sidoravicius, Balazs Rath
In the present note we analyze the one-dimensional multi-particle diffusion limited aggregation (MDLA) model: the initial number of particles at each positive integer site has Pois…
A moment-generating formula for Erdős-Rényi component sizes
Balazs Rath
We derive a simple formula characterizing the distribution of the size of the connected component of a fixed vertex in the Erdős-Rényi random graph which allows us to give elementa…
Rigid representations of the multiplicative coalescent with linear deletion
James B. Martin, Balazs Rath
We introduce the multiplicative coalescent with linear deletion, a continuous-time Markov process describing the evolution of a collection of blocks. Any two blocks of sizes an…
Feller property of the multiplicative coalescent with linear deletion
Balazs Rath
We modify the definition of Aldous' multiplicative coalescent process and introduce the multiplicative coalescent with linear deletion (MCLD). A state of this process is a square-s…
Percolation on the stationary distributions of the voter model
Balazs Rath, Daniel Valesin
The voter model on is a particle system that serves as a rough model for changes of opinions among social agents or, alternatively, competition between biological sp…
A short proof of the phase transition for the vacant set of random interlacements
Balazs Rath
The vacant set of random interlacements at level , introduced in arXiv:0704.2560, is a percolation model on , which arises as the set of sites avoided…
On decoupling inequalities and percolation of excursion sets of the Gaussian free field
Serguei Popov, Balazs Rath
We prove decoupling inequalities for the Gaussian free field on , . As an application, we obtain exponential decay (with logarithmic correction for ) of…
On chemical distances and shape theorems in percolation models with long-range correlations
Alexander Drewitz, Balazs Rath, Artem Sapozhnikov
In this paper we provide general conditions on a one parameter family of random infinite subsets of Z^d to contain a unique infinite connected component for which the chemical dist…
Local percolative properties of the vacant set of random interlacements with small intensity
Alexander Drewitz, Balazs Rath, Artem Sapozhnikov
Random interlacements at level u is a one parameter family of connected random subsets of Z^d, d>=3 introduced in arXiv:0704.2560. Its complement, the vacant set at level u, exhibi…
An equation-free approach to coarse-graining the dynamics of networks
Katherine A. Bold, Karthikeyan Rajendran, Balázs Ráth +1
We propose and illustrate an approach to coarse-graining the dynamics of evolving networks (networks whose connectivity changes dynamically). The approach is based on the equation-…
The effect of small quenched noise on connectivity properties of random interlacements
Balazs Rath, Artem Sapozhnikov
The random interlacements (at level u) is a one parameter family of random subsets of Z^d introduced by Sznitman in arXiv:0704.2560. The vacant set at level u is the complement of…
Multigraph limit of the dense configuration model and the preferential attachment graph
Balazs Rath, Laszlo Szakacs
The configuration model is the most natural model to generate a random multigraph with a given degree sequence. We use the notion of dense graph limits to characterize the special…
Limits of permutation sequences
Carlos Hoppen, Yoshiharu Kohayakawa, Carlos Gustavo Moreira +2
A permutation sequence is said to be convergent if the density of occurrences of every fixed permutation in the elements of the sequence converges. We prove that such a convergent…
Time evolution of dense multigraph limits under edge-conservative preferential attachment dynamics
Balazs Rath
We define the edge reconnecting model, a random multigraph evolving in time. At each time step we change one endpoint of a uniformly chosen edge: the new endpoint is chosen by line…
Multigraph limits and exchangeability
Istvan Kolossvary, Balazs Rath
The theory of limits of dense graph sequences was initiated by Lovasz and Szegedy. We give a possible generalization of this theory to multigraphs. Our proofs are based on the corr…
Mean field frozen percolation
Balazs Rath
We define a modification of the Erdos-Renyi random graph process which can be regarded as the mean field frozen percolation process. We describe the behavior of the process using d…
Erdos-Renyi random graphs + forest fires = self-organized criticality
Balazs Rath, Balint Toth
We modify the usual Erdos-Renyi random graph evolution by letting connected clusters 'burn down' (i.e. fall apart to disconnected single sites) due to a Poisson flow of lightnings.…