14 citations · 30 across the 14 of their papers we have counts for
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An OSSS-type inequality for uniformly drawn subsets of fixed size
Jacob van den Berg, Henk Don
The OSSS inequality [O'Donnell, Saks, Schramm and Servedio, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05), Pittsburgh (2005)] gives an upper bound for the…
Boundary rules and breaking of self-organized criticality in 2D frozen percolation
Jacob van den Berg, Pierre Nolin
We study frozen percolation on the (planar) triangular lattice, where connected components stop growing ("freeze") as soon as their "size" becomes at least , for some parameter…
Stochastic Domination in Space-Time for the Contact Process
Jacob van den Berg, Stein Andreas Bethuelsen
Liggett and Steif (2006) proved that, for the supercritical contact process on certain graphs, the upper invariant measure stochastically dominates an i.i.d.\ Bernoulli product mea…
Two-dimensional volume-frozen percolation: deconcentration and prevalence of mesoscopic clusters
Jacob van den Berg, Demeter Kiss, Pierre Nolin
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 la…
The expected number of critical percolation clusters intersecting a line segment
Jacob van den Berg, Rene Conijn
We study critical percolation on a regular planar lattice. Let be the expected number of open clusters intersecting or hitting the line segment . (For the subscript…
Two-dimensional volume-frozen percolation: exceptional scales
Jacob van den Berg, Pierre Nolin
We study a percolation model on the square lattice, where clusters "freeze" (stop growing) as soon as their volume (i.e. the number of sites they contain) gets larger than N, the p…
The gaps between the sizes of large clusters in 2D critical percolation
Jacob van den Berg, Rene Conijn
Consider critical bond percolation on a large 2n by 2n box on the square lattice. It is well-known that the size (i.e. number of vertices) of the largest open cluster is, with high…
Sharpness versus robustness of the percolation transition in 2D contact processes
J. van den Berg, J. E. Björnberg, M. Heydenreich
We study versions of the contact process with three states, and with infections occurring at a rate depending on the overall infection density. Motivated by a model described in [1…
Escape of resources in distributed clustering processes
J. van den Berg, M. R. Hilário, Alexander E. Holroyd
In a distributed clustering algorithm introduced by Coffman, Courtois, Gilbert and Piret \cite{coffman91}, each vertex of receives an initial amount of a resource, a…
Sublinearity of the travel-time variance for dependent first-passage percolation
Jacob van den Berg, Demeter Kiss
Let be the set of edges of the -dimensional cubic lattice , with , and let , be nonnegative values. The passage time from a vertex to…
A percolation process on the square lattice where large finite clusters are frozen
Jacob van den Berg, Bernardo N. B. de Lima, Pierre Nolin
Aldous constructed a growth process for the binary tree where clusters freeze as soon as they become infinite. It was pointed out by Benjamini and Schramm that such a process does…
Sharpness of the percolation transition in the two-dimensional contact process
J. van den Berg
For ordinary (independent) percolation on a large class of lattices it is well known that below the critical percolation parameter the cluster size distribution has exponenti…
The size of a pond in 2D invasion percolation
Jacob van den Berg, Antal A. Járai, Bálint Vágvölgyi
We consider invasion percolation on the square lattice. It has been proved by van den Berg, Peres, Sidoravicius and Vares, that the probability that the radius of a so-called pond…
Proof of a conjecture of N. Konno for the 1D contact process
J. van den Berg, O. Häggström, J. Kahn
Consider the one-dimensional contact process. About ten years ago, N. Konno stated the conjecture that, for all positive integers , the upper invariant measure has the followi…