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math.PR2003★ 136 cited
On the scaling of the chemical distance in long-range percolation models
Marek Biskup
We consider the (unoriented) long-range percolation on Z^d in dimensions d\ge1, where distinct sites x,y\in Z^d get connected with probability p_{xy}\in[0,1]. Assuming p_{xy}=|x-y|…
math.PR2002★ 46 cited
Rigorous analysis of discontinuous phase transitions via mean-field bounds
Marek Biskup, Lincoln Chayes
We consider a variety of nearest-neighbor spin models defined on the d-dimensional hypercubic lattice Z^d. Our essential assumption is that these models satisfy the condition of re…
math.PR2002★ 3 cited
Phase transition and critical behavior in a model of organized criticality
Marek Biskup, Philippe Blanchard, Lincoln Chayes +2
We study a model of ``organized'' criticality, where a single avalanche propagates through an \textit{a priori} static (i.e., organized) sandpile configuration. The latter is chose…