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pro vyhledávání: '"Berg, J. Van Den"'
Autor:
Berg, J. van den, Don, H.
Consider critical site percolation on $\mathbb{Z}^d$ with $d \geq 2$. We prove a lower bound of order $n^{- d^2}$ for point-to-point connection probabilities, where $n$ is the distance between the points. Most of the work in our proof concerns a `con
Externí odkaz:
http://arxiv.org/abs/1912.10964
The main result of this paper is the following: if F is any field and R is any F-subalgebra of the algebra of nxn matrices over F with Lie nilpotence index m, then the F-dimension of R is less or equal than M(m+1,n), where M(m+1,n) is the maximum of
Externí odkaz:
http://arxiv.org/abs/1608.04562
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 [17] for vegetation patterns in arid landscapes, we focus on percolation
Externí odkaz:
http://arxiv.org/abs/1306.1032
Autor:
Berg, J. van den, Gandolfi, A.
Recently, van den Berg and Jonasson gave the first substantial extension of the BK inequality for non-product measures: they proved that, for k-out-of-n measures, the probability that two increasing events occur disjointly is at most the product of t
Externí odkaz:
http://arxiv.org/abs/1203.3665
Autor:
Berg, J. van den, Jonasson, J.
The BK inequality (\cite{BK85}) says that,for product measures on $\{0,1\}^n$, the probability that two increasing events $A$ and $B$ `occur disjointly' is at most the product of the two individual probabilities. The conjecture in \cite{BK85} that th
Externí odkaz:
http://arxiv.org/abs/1105.3862
In a distributed clustering algorithm introduced by Coffman, Courtois, Gilbert and Piret \cite{coffman91}, each vertex of $\mathbb{Z}^d$ receives an initial amount of a resource, and, at each iteration, transfers all of its resource to the neighborin
Externí odkaz:
http://arxiv.org/abs/1008.2426
Autor:
Berg, J. van den
Publikováno v:
Annals of Applied Probability 2011, Vol. 21, No. 1, 374-395
For ordinary (independent) percolation on a large class of lattices it is well known that below the critical percolation parameter $p_c$ the cluster size distribution has exponential decay and that power-law behavior of this distribution can only occ
Externí odkaz:
http://arxiv.org/abs/0907.2843
Autor:
Berg, J. van den
Publikováno v:
Annals of Probability 2008, Vol. 36, No. 5, 1880-1903
One of the most well-known classical results for site percolation on the square lattice is the equation $p_c+p_c^*=1$. In words, this equation means that for all values $\neq p_c$ of the parameter $p$, the following holds: either a.s. there is an inf
Externí odkaz:
http://arxiv.org/abs/0809.4184
Autor:
Berg, J. van den, de Lima, B. N. B.
The self-destructive percolation model is defined as follows: Consider percolation with parameter $p > p_c$. Remove the infinite occupied cluster. Finally, give each vertex (or, for bond percolation, each edge) that at this stage is vacant, an extra
Externí odkaz:
http://arxiv.org/abs/0711.3563
We study models of spatial growth processes where initially there are sources of growth (indicated by the colour green) and sources of a growth-stopping (paralyzing) substance (indicated by red). The green sources expand and may merge with others (th
Externí odkaz:
http://arxiv.org/abs/0706.0219