Shape transition under excess self-intersections for transient random walk
Annales de l'I.H.P. Probabilités et statistiques (2010)
- Volume: 46, Issue: 1, page 250-278
- ISSN: 0246-0203
Access Full Article
topAbstract
topHow to cite
topAsselah, Amine. "Shape transition under excess self-intersections for transient random walk." Annales de l'I.H.P. Probabilités et statistiques 46.1 (2010): 250-278. <http://eudml.org/doc/240710>.
@article{Asselah2010,
abstract = {We reveal a shape transition for a transient simple random walk forced to realize an excess q-norm of the local times, as the parameter q crosses the value qc(d)=d/(d−2). Also, as an application of our approach, we establish a central limit theorem for the q-norm of the local times in dimension 4 or more.},
author = {Asselah, Amine},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {self-intersection local times; large deviations; random walk; random environment; self-intersection local time; large deviation; two-fold intersection; transient random walk; shape transition},
language = {eng},
number = {1},
pages = {250-278},
publisher = {Gauthier-Villars},
title = {Shape transition under excess self-intersections for transient random walk},
url = {http://eudml.org/doc/240710},
volume = {46},
year = {2010},
}
TY - JOUR
AU - Asselah, Amine
TI - Shape transition under excess self-intersections for transient random walk
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2010
PB - Gauthier-Villars
VL - 46
IS - 1
SP - 250
EP - 278
AB - We reveal a shape transition for a transient simple random walk forced to realize an excess q-norm of the local times, as the parameter q crosses the value qc(d)=d/(d−2). Also, as an application of our approach, we establish a central limit theorem for the q-norm of the local times in dimension 4 or more.
LA - eng
KW - self-intersection local times; large deviations; random walk; random environment; self-intersection local time; large deviation; two-fold intersection; transient random walk; shape transition
UR - http://eudml.org/doc/240710
ER -
References
top- [1] M. Aizenman. The intersection of Brownian paths as a case study of a renormalization group method for quantum field theory. Comm. Math. Phys. 97 (1985) 91–110. Zbl0573.60076MR782960
- [2] A. Asselah. Large deviations principle for the self-intersection local times for simple random walk in dimension 5 or more. Preprint, 2007. Available at: arXiv:0707.0813.
- [3] A. Asselah. Large deviations for the Self-intersection local times for simple random walk in dimension d=3. Probab. Theory Related Fields 141 (2008) 19–45. Zbl1135.60340MR2372964
- [4] A. Asselah and F. Castell. A note on random walk in random scenery. Ann. Inst. H. Poincaré 43 (2007) 163–173. Zbl1112.60088MR2303117
- [5] A. Asselah and F. Castell. Random walk in random scenery and self-intersection local times in dimensions d≥5. Probab. Theory Related Fields 138 (2007) 1–32. Zbl1116.60057MR2288063
- [6] M. Becker and W. König. Moments and distribution of the local times of a transient random walk on ℤd. J. Theoret. Probab. 22 (2009) 365–374. Zbl1175.60043MR2501325
- [7] P. Billingsley. Probability and Measure. Wiley, New York, 1979. Zbl0649.60001MR534323
- [8] E. Bolthausen and U. Schmock. On self-attracting d-dimensional random walks. Ann. Probab. 25 (1997) 531–572. Zbl0873.60008MR1434118
- [9] D. C. Brydges and G. Slade. The diffusive phase of a model of self-interacting walks. Probab. Theory Related Fields 103 (1995) 285–315. Zbl0832.60096MR1358079
- [10] X. Chen. Limit laws for the energy of a charged polymer. Ann. Inst. H. Poincaré Probab. Statist. 44 (2008) 638–672. Zbl1178.60024MR2446292
- [11] X. Chen. Random walk intersections: Large deviations and some related topics. 2009. To appear. Zbl1192.60002MR2584458
- [12] A. Dvoretzky and P. Erdös. Some problems on random walk in space. In Proc. Berkeley Symposium 1951353–367. Univ. California Press, Berkeley, 1951. Zbl0044.14001MR47272
- [13] S. Edwards. The statistical mechanics of polymers with excluded volume. Proc. Phys. Sci 85 (1965) 613–624. Zbl0125.23205MR183442
- [14] G. Felder and J. Frölich. Intersection properties of simple random walks: A renormalization group approach. Comm. Math. Phys. 97 (1985) 111–124. Zbl0573.60065MR782961
- [15] K. Fleischmann, P. Mörters and V. Wachtel. Moderate deviations for random walk in random scenery. Stochastic Process. Appl. 118 (2008) 1768–1802. Zbl1157.60020MR2454464
- [16] N. C. Jain and W. E. Pruitt. The range of transient random walk. J. Anal. Math. 24 (1971) 369–393. Zbl0249.60038MR283890
- [17] G. Lawler. Intersection of Random Walks. Probability and Its Applications. Birkhäuser, Boston, MA, 1991. Zbl0925.60078MR1117238
- [18] J.-F. Le Gall. Propriétés d’intersection des marches aléatoires. Comm. Math. Phys. 104 (1985) 471–507. Zbl0609.60078MR840748
- [19] J.-F. Le Gall. Sur le temps local d’intersection du mouvement brownien plan et la méthode de renormalisation de Varadhan. Séminaire de probabilités de Strasbourg 19 (1985) 314–331. Zbl0563.60072MR889492
- [20] J.-F. Le Gall and J. Rosen. The range of stable random walks. Ann. Probab. 19 (1991) 650–705. Zbl0729.60066MR1106281
- [21] M. J. Westwater. On Edwards’ model for long polymer chains. Comm. Math. Phys. 72 (1980) 131–174. Zbl0431.60100MR573702
- [22] S. R. S. Varadhan. Appendix to Euclidean quantum field theory by K.Symanzik. In Local Quantum Field Theory. R. Jost (Ed.). Academic Press, New York, 1966.
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.