Graham, Benjamin T.. (2012) Sublinear variance for directed last-passage percolation. Journal of Theoretical Probability, Vol.25 (No.3). pp. 687-702. ISSN 0894-9840

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Abstract

A range of first-passage percolation type models are believed to demonstrate the related properties of sublinear variance and superdiffusivity. We show that directed last-passage percolation with Gaussian vertex weights has a sublinear variance property. We also consider other vertex weight distributions. Corresponding results are obtained for the ground state of the “directed polymers in a random environment” model.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Percolation (Statistical physics), Convex domains
Journal or Publication Title:	Journal of Theoretical Probability
Publisher:	Springer New York LLC
ISSN:	0894-9840
Date:	2012
Volume:	Vol.25
Number:	No.3
Page Range:	pp. 687-702
Identification Number:	10.1007/s10959-010-0315-6
Status:	Peer Reviewed
Publication Status:	Published
References:	1. Baik, J., Deift, P., McLaughlin, K.T.-R., Miller, P., Zhou, X.: Optimal tail estimates for directed last passage site percolation with geometric random variables. Adv. Theor. Math. Phys. 5(6), 1207–1250 (2001) 2. Benaïm, M., Rossignol, R.: Exponential concentration for first passage percolation through modified Poincaré inequalities. Ann. Inst. Henri Poincaré Probab. Stat. 44(3), 544–573 (2008) 3. Benjamini, I., Kalai, G., Schramm, O.: First passage percolation has sublinear distance variance. Ann. Probab. 31(4), 1970–1978 (2003) 4. Chatterjee, S.: Chaos, concentration, and multiple valleys. arXiv:0810.4221 (2008) 5. Comets, F., Shiga, T., Yoshida, N.: Probabilistic analysis of directed polymers in a random environment: a review. Adv. Stud. Pure Math. 39, 115–142 (2004) 6. Johansson, K.: Shape fluctuations and random matrices. Commun. Math. Phys. 209(2), 437–476 (2000) 7. Johansson, K.: Transversal fluctuations for increasing subsequences on the plane. Probab. Theory Relat. Fields 116(4), 445–456 (2000) 8. Martin, J.B.: Limiting shape for directed percolation models. Ann. Probab. 32(4), 2908–2937 (2004) 9. Martin, J.B.: Last-passage percolation with general weight distribution. Markov Process. Relat. Fields 12(2), 273–299 (2006) 10. Piza, M.S.T.: Directed polymers in a random environment: some results on fluctuations. J. Stat. Phys. 89(3–4), 581–603 (1997) 11. Talagrand, M.: On Russo’s approximate zero-one law. Ann. Probab. 22(3), 1576–1587 (1994)
URI:	http://wrap.warwick.ac.uk/id/eprint/41074

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