Poisson Broken Lines Process and its Application to Bernoulli First Passage Percolation |
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| Authors: | V Sidoravicius M E Vares D Surgailis |
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| Institution: | (1) IMPA, Estr. Dona Castorina 110, Rio De Janeiro, Brazil. e-mail;(2) Institute of Mathematics and Informatics, Akademijos 4, LT-2600 Vilnius, and;(3) Department of Mathematics,  iauliai University, Vi inskio 25, LT-5400 iauliai, Lithuania. e-mail |
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| Abstract: | In this note we introduce a process, which we call 'the Poisson broken lines process", and we compute the intensity of a point process which is obtained by intersecting the Poisson broken lines process with an abscissa axis. In the second part we apply this result to compute an explicit lower bound for the time constant of a planar Bernoulli first passage percolation model with the parameter p < pc. |
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| Keywords: | first passage percolation time constant Poisson broken lines process |
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