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First passage percolation and escape strategies
Author(s) -
Andjel Enrique D.,
Vares Maria E.
Publication year - 2015
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20548
Subject(s) - percolation (cognitive psychology) , path (computing) , mathematics , combinatorics , distribution (mathematics) , percolation theory , struct , statistical physics , geodesic , physics , mathematical analysis , topology (electrical circuits) , computer science , neuroscience , programming language , biology
Consider first passage percolation onℤ dwith passage times given by i.i.d. random variables with common distribution F . Lett π ( u , v ) be the time from u to v for a path π and t ( u , v ) the minimal time among all paths from u to v . We ask whether or not there exist points x , y ∈ ℤ dand a semi‐infinite path π = ( y 0 = y , y 1 , … ) such thatt π ( y , y n + 1 ) < t ( x , y n ) for all n . Necessary and sufficient conditions on F are given for this to occur. When the support of F is unbounded, we also obtain results on the number of edges with large passage time used by geodesics. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 414–423, 2015