Point-to-point distance in first passage percolation on (Tree)xZ

Itai Benjamini; Pascal Maillard

doi:10.1007/978-3-319-09477-9_3

Point-to-point distance in first passage percolation on (Tree)xZ

Itai Benjamini, Pascal Maillard

Department of Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

We consider first passage percolation (FPP) on T_dx G, where T_d is the d-regular tree (d ≥ 3)and G is a graph containing an infinite ray 0,1,2,….It is shown that for a fixed vertex v in the tree, the fluctuation of the distance in the FPP metric between the points (v, 0) and (v, n) is of the order of at most log n. We conjecture that the real fluctuations are of order 1 and explain why.

Original language	English
Pages (from-to)	47-51
Number of pages	5
Journal	Lecture Notes in Mathematics
Volume	2116
DOIs	https://doi.org/10.1007/978-3-319-09477-9_3
State	Published - 1 Jan 2014

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1007/978-3-319-09477-9_3

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abstract = "We consider first passage percolation (FPP) on Tdx G, where Td is the d-regular tree (d ≥ 3)and G is a graph containing an infinite ray 0,1,2,….It is shown that for a fixed vertex v in the tree, the fluctuation of the distance in the FPP metric between the points (v, 0) and (v, n) is of the order of at most log n. We conjecture that the real fluctuations are of order 1 and explain why.",

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N2 - We consider first passage percolation (FPP) on Tdx G, where Td is the d-regular tree (d ≥ 3)and G is a graph containing an infinite ray 0,1,2,….It is shown that for a fixed vertex v in the tree, the fluctuation of the distance in the FPP metric between the points (v, 0) and (v, n) is of the order of at most log n. We conjecture that the real fluctuations are of order 1 and explain why.

AB - We consider first passage percolation (FPP) on Tdx G, where Td is the d-regular tree (d ≥ 3)and G is a graph containing an infinite ray 0,1,2,….It is shown that for a fixed vertex v in the tree, the fluctuation of the distance in the FPP metric between the points (v, 0) and (v, n) is of the order of at most log n. We conjecture that the real fluctuations are of order 1 and explain why.

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JO - Lecture Notes in Mathematics

JF - Lecture Notes in Mathematics

ER -

Point-to-point distance in first passage percolation on (Tree)xZ

Abstract

All Science Journal Classification (ASJC) codes

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