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Upper bound on the disconnection time of discrete cylinders and random interlacements. (English) Zbl 1179.60025
The paper derives an upper bound for the disconnection time of a discrete cylinder with a base defined by a \(d\)-dimensional torus of large side-length. Some relations with percolation and random interlacements are exhibited. Several results on the disconnection time caused by simple random walk of discrete cylinders with various large bases are obtained, and their proofs use stochastic domination arguments.

MSC:
60G50 Sums of independent random variables; random walks
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics
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