A Note on a Problem by Welsh in First-Passage Percolation

1998 ◽  
Vol 7 (1) ◽  
pp. 11-15 ◽  
Author(s):  
SVEN ERICK ALM
Keyword(s):  
First Passage Times ◽  
Square Lattice ◽  
Trivial Case ◽  
First Passage Percolation ◽  
First Passage ◽  
General Proof ◽  
Mean First Passage Times ◽  
The Subject ◽  
Passage Times

Consider first-passage percolation on the square lattice. Welsh, who together with Hammersley introduced the subject in 1963, has formulated a problem about mean first-passage times, which, although seemingly simple, has not been proved in any non-trivial case. In this paper we give a general proof of Welsh's problem.

First-passage percolation on the square lattice, II

1977 ◽  
Vol 9 (2) ◽  
pp. 283-295 ◽  
Author(s):  
John C. Wierman
Keyword(s):  
Sufficient Conditions ◽  
Initial Result ◽  
First Passage Times ◽  
Square Lattice ◽  
Maximum Height ◽  
First Passage Percolation ◽  
First Passage ◽  
Necessary And Sufficient ◽  
Passage Times

Several problems are considered in the theory of first-passage percolation on the two-dimensional integer lattice. The results include: (i) necessary and sufficient conditions for the existence of moments of first-passage times; (ii) determination of an upper bound for the time constant; (iii) an initial result concerning the maximum height of routes for first-passage times; (iv) ergodic theorems for a class of reach processes.

First-passage percolation on the square lattice, II

1977 ◽  
Vol 9 (02) ◽  
pp. 283-295 ◽  
Author(s):  
John C. Wierman
Keyword(s):  
Sufficient Conditions ◽  
Initial Result ◽  
First Passage Times ◽  
Square Lattice ◽  
Maximum Height ◽  
First Passage Percolation ◽  
First Passage ◽  
Necessary And Sufficient ◽  
Passage Times

Several problems are considered in the theory of first-passage percolation on the two-dimensional integer lattice. The results include: (i) necessary and sufficient conditions for the existence of moments of first-passage times; (ii) determination of an upper bound for the time constant; (iii) an initial result concerning the maximum height of routes for first-passage times; (iv) ergodic theorems for a class of reach processes.

scholarly journals Correlation functions, mean first passage times, and the Kemeny constant

2020 ◽  
Vol 152 (10) ◽  
pp. 104108 ◽  
Author(s):  
Adam Kells ◽  
Vladimir Koskin ◽  
Edina Rosta ◽  
Alessia Annibale
Keyword(s):  
Correlation Functions ◽  
First Passage Times ◽  
First Passage ◽  
Mean First Passage Times ◽  
Passage Times

scholarly journals RaTrav: a tool for calculating mean first-passage times on biochemical networks

2013 ◽  
Vol 7 (1) ◽  
pp. 130 ◽  
Author(s):  
Mieczyslaw Torchala ◽  
Przemyslaw Chelminiak ◽  
Michal Kurzynski ◽  
Paul A Bates
Keyword(s):  
First Passage Times ◽  
Biochemical Networks ◽  
First Passage ◽  
Mean First Passage Times ◽  
Passage Times

scholarly journals Calculating Mean First Passage Times from Markov Models of Proteins

2007 ◽  
Author(s):  
Christian H. Jensen ◽  
Dmitry Nerukh ◽  
Robert C. Glen ◽  
Arno P. J. M. Siebes ◽  
Michael R. Berthold ◽  
...  
Keyword(s):  
Markov Models ◽  
First Passage Times ◽  
First Passage ◽  
Mean First Passage Times ◽  
Passage Times
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