Directed polymer in random environment and last passage percolation*

Philippe Carmona

ESAIM: Probability and Statistics (2010)

  • Volume: 14, page 263-270
  • ISSN: 1292-8100

Abstract

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The sequence of random probability measures νn that gives a path of length n, 1 n times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the Legendre transform of the free energy of the associated directed polymer in a random environment. Consequences on the asymptotics of the typical number of paths whose collected weight is above a fixed proportion are then drawn.

How to cite

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Carmona, Philippe. "Directed polymer in random environment and last passage percolation*." ESAIM: Probability and Statistics 14 (2010): 263-270. <http://eudml.org/doc/250855>.

@article{Carmona2010,
abstract = {The sequence of random probability measures νn that gives a path of length n, $\frac\{1\}\{n\}$ times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the Legendre transform of the free energy of the associated directed polymer in a random environment. Consequences on the asymptotics of the typical number of paths whose collected weight is above a fixed proportion are then drawn. },
author = {Carmona, Philippe},
journal = {ESAIM: Probability and Statistics},
keywords = {Directed polymer; random environment; partition function; last passage percolation; directed polymer},
language = {eng},
month = {10},
pages = {263-270},
publisher = {EDP Sciences},
title = {Directed polymer in random environment and last passage percolation*},
url = {http://eudml.org/doc/250855},
volume = {14},
year = {2010},
}

TY - JOUR
AU - Carmona, Philippe
TI - Directed polymer in random environment and last passage percolation*
JO - ESAIM: Probability and Statistics
DA - 2010/10//
PB - EDP Sciences
VL - 14
SP - 263
EP - 270
AB - The sequence of random probability measures νn that gives a path of length n, $\frac{1}{n}$ times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the Legendre transform of the free energy of the associated directed polymer in a random environment. Consequences on the asymptotics of the typical number of paths whose collected weight is above a fixed proportion are then drawn.
LA - eng
KW - Directed polymer; random environment; partition function; last passage percolation; directed polymer
UR - http://eudml.org/doc/250855
ER -

References

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  10. A. Dembo and O. Zeitouni, Large deviations techniques and applications. Second edition. Volume 38 of Applications of Mathematics (New York). Springer-Verlag, New York (1998). MR MR1619036.  
  11. J. Feng and T.G. Kurtz, Large deviations for stochastic processes, in Mathematical Surveys and Monographs, volume 131. American Mathematical Society, Providence, RI (2006). MR MR2260560.  
  12. H. Kesten and V. Sidoravivius, A problem in last-passage percolation, preprint (2007), .  URIhttp://arxiv.org/abs/0706.3626
  13. S.R.S. Varadhan, Large deviations for random walks in a random environment. Commun. Pure Appl. Math.56 (2003) 1222–1245. Dedicated to the memory of Jürgen K. Moser. MR MR1989232.  

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