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Using our new Boolean representing for random graphs, dated since 1995 and introduced in [5], [6], [7], we apply it, at Cebˆı¸sev in- equality and a weak convergence in
In an n by n complete bipartite graph with independent exponentially distributed edge costs, we ask for the minimum total cost of a set of edges of which each vertex is incident to
Then, to prove IDLA inner bound, we need to show that for each vertex v ∈ V the Green function from 0 and expected exit time from a ball around 0 of a random walk starting at v ,
For a much-studied model of random copolymer at a selective interface we prove that the slope of the critical curve in the weak-disorder limit is strictly smaller than 1, which is
It remains to find an upper bound for the second term. Thus, we can rewrite the r.h.s. and have the same law as the number of vertices visited by the walk before the time D of its
Yaglom, Some classes of random fields in n-dimensional space, related to stationary random processes, Theory of Probability and its Applications 2
If a random walk characterized by conductances is started at the root of a tree, it is well known [3] that the escape probability equals the ratio of the effective conductance of
At the end of this note we show that (2) is not true in three dimensions, i.e., with probability one, the cut points of two independent three dimensional simple random walks
