English
Freezing and decorated Poisson point processes
Post-edited
Auteurs : Zeitouni, Ofer (Auteur de la conférence)
CIRM (Editeur )
60G55 - Point processes
60J65 - Brownian motion
60J80 - Branching processes (Galton-Watson, birth-and-death, etc.)
CIRM (Editeur )
Résumé :
The freezing in the title refers to a property of point processes: let $\left ( X_i \right )_{i\geq 1}$ denote a point process which is locally finite and has finite maximum. For a function f continuous of compact support, define $Z_f=f\left ( X_1 \right )+f\left ( X_2 \right )+....$ We say that freezing occurs if the Laplace transform of $Z_f$ depends on f only through a shift. I will discuss this notion and its equivalence with other properties of the point process. In particular, such freezing occurs for the extremal process in branching random walks and in certain versions of the (discrete) two dimensional GFF.
Joint work with Eliran Subag
Codes MSC : Joint work with Eliran Subag
60G55 - Point processes
60J65 - Brownian motion
60J80 - Branching processes (Galton-Watson, birth-and-death, etc.)
|
Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 16/06/14 Date de Captation : 02/06/14 Sous Collection : Research talks Catégorie arXiv : Probability Domaine(s) : Probabilités & Statistiques Format : QuickTime (.mov) Durée : 01:12:04 Audience : Chercheurs Download : https://videos.cirm-math.fr/2014-06-02_Zeitouni.mp4 
|
Informations sur la Rencontre
Nom de la Rencontre : Recent models in random media / Modèles récents en milieu aléatoireOrganisateurs de la Rencontre : Enriquez, Nathanaël ; Hu, Yueyun ; Shi, Zhan Dates : 02/06/14 - 06/06/14 Année de la rencontre : 2014 URL de la Rencontre : http://www.math.univ-paris13.fr/~tournie...
Données de citation
DOI : 10.24350/CIRM.V.18503803Citer cette vidéo: Zeitouni, Ofer (2014). Freezing and decorated Poisson point processes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18503803 URI : http://dx.doi.org/10.24350/CIRM.V.18503803 |
Bibliographie
- E. Aïdékon, J. Berestycki, É. Brunet, and Z. Shi, Branching Brownian motion seen from its tip, Probab. Theory Related Fields 157 (2013), no. 1-2, 405-451 - http://www.ams.org/mathscinet-getitem?mr=3101852
- R. Allez, R. Rhodes, and V. Vargas, Lognormal *-scale invariant random measures, Probab. Theory Related Fields 155 (2013), no. 3-4, 751-788 - http://www.ams.org/mathscinet-getitem?mr=3034792
- L.-P. Arguin, A. Bovier, and N. Kistler, Genealogy of extremal particles of branching Brownian motion, Comm. Pure Appl. Math. 64 (2011), no. 12, 1647-1676 - http://www.ams.org/mathscinet-getitem?mr=2838339
- L.-P. Arguin, A. Bovier, and N. Kistler, Poissonian statistics in the extremal process of branching Brownian motion, Ann. Appl. Probab. 22 (2012), no. 4, 1693-1711 - http://www.ams.org/mathscinet-getitem?mr=2985174
- L.-P. Arguin, A. Bovier, and N. Kistler, An ergodic theorem for the frontier of branching Brownian motion, Electron. J. Probab. 18 (2013), no. 53, 25 - http://www.ams.org/mathscinet-getitem?mr=3065863
- L.-P. Arguin, A. Bovier, and N. Kistler, The extremal process of branching Brownian motion, Probab. Theory Related Fields 157 (2013), no. 3-4, 535-574 - http://www.ams.org/mathscinet-getitem?mr=3129797
- L.-P. Arguin and Z. Olivier, Poisson-Dirichlet statistics for the extremes of a log-correlated Gaussian field, preprint - http://arxiv.org/abs/1203.4216
- M. Biskup and O. Louidor, Extreme local extrema of two-dimensional discrete gaussian free field, preprint - http://arxiv.org/abs/1306.2602
- A. Bovier and L. Hartung, The extremal process of two-speed branching brownian motion, preprint - http://arxiv.org/abs/1308.1868
- M. Bramson, Maximal displacement of branching Brownian motion, Comm. Pure Appl. Math. 31 (1978), no. 5, 531-581 - http://www.ams.org/mathscinet-getitem?mr=0494541
- M. Bramson, Convergence of solutions of the Kolmogorov equation to travelling waves, Mem. Amer. Math. Soc. 44 (1983), no. 285, iv+190 - http://www.ams.org/mathscinet-getitem?mr=705746
- M. Bramson, J. Ding, and O. Zeitouni, Convergence in law of the maximum of the two-dimensional discrete gaussian free field, preprint - http://arxiv.org/abs/1301.6669
- É. Brunet and B. Derrida, A branching random walk seen from the tip, J. Stat. Phys. 143 (2011), no. 3, 420-446 - http://www.ams.org/mathscinet-getitem?mr=2799946
- É. Brunet and B. Derrida, A branching random walk seen from the tip, preprint - http://arxiv.org/abs/1011.4864
- J. L. Cardy, Conformal invariance and statistical mechanics, Champs, cordes et phénomènes critiques (Les Houches, 1988), North-Holland, Amsterdam, 1990, pp. 169-245 - http://www.ams.org/mathscinet-getitem?mr=1052933
- D. Carpentier and P. Le Doussal, Glass transition of a particle in a random potential, front selection in nonlinear renormalization group, and entropic phenomena in liouville and sinhgordon models, Phys. Rev. E 63 (2001), 026110 - http://dx.doi.org/10.1103/PhysRevE.63.026110
- B. Chauvin and A. Rouault, Supercritical branching Brownian motion and K-P-P equation in the critical speed-area, Math. Nachr. 149 (1990), 41-59 - http://www.ams.org/mathscinet-getitem?mr=1124793
- M. G. Darboux, Sur le théorème fondamental de la géométrie projective, Math. Ann. 17 (1880), no. 1, 55-61 - http://www.ams.org/mathscinet-getitem?mr=1510050
- Y. Davydov, I. Molchanov, and S. Zuyev, Strictly stable distributions on convex cones, Electron. J. Probab. 13 (2008), no. 11, 259-321 - http://www.ams.org/mathscinet-getitem?mr=2386734
- L. de Haan and A. Ferreira, Extreme value theory, Springer Series in Operations Research and Financial Engineering, Springer, New York, 2006, An introduction - http://www.ams.org/mathscinet-getitem?mr=2234156
- A. Dembo and O. Zeitouni, Large deviations techniques and applications, second ed., Applications of Mathematics (New York), vol. 38, Springer-Verlag, New York, 1998 - http://www.ams.org/mathscinet-getitem?mr=1619036
- B. Derrida, Random-energy model: an exactly solvable model of disordered systems, Phys. Rev. B (3) 24 (1981), no. 5, 2613-2626 - http://www.ams.org/mathscinet-getitem?mr=627810
- B. Derrida and H. Spohn, Polymers on disordered trees, spin glasses, and traveling waves, J. Statist. Phys. 51 (1988), no. 5-6, 817-840, New directions in statistical mechanics (Santa Barbara, CA, 1987) - http://www.ams.org/mathscinet-getitem?mr=971033
- P. Di Francesco, P. Mathieu, and D. Sénéchal, Conformal field theory, Graduate Texts in Contemporary Physics, Springer-Verlag, New York, 1997 - http://www.ams.org/mathscinet-getitem?mr=1424041
- B. Duplantier, R. Rhodes, S. Sheffield, and V. Vargas, Critical gaussian multiplicative chaos: Convergence of the derivative martingale, preprint - http://arxiv.org/abs/1206.1671
- W. Feller, An introduction to probability theory and its applications. Vol. II., Second edition, John Wiley & Sons Inc., New York, 1971 - http://www.ams.org/mathscinet-getitem?mr=0270403
- R. Fernández, J. Fröhlich, and A. D. Sokal, Random walks, critical phenomena, and triviality in quantum field theory, Texts and Monographs in Physics, Springer-Verlag, Berlin, 1992 - http://www.ams.org/mathscinet-getitem?mr=1219313
- Y. V. Fyodorov, Multifractality and freezing phenomena in random energy landscapes: An introduction, Physica A: Statistical Mechanics and its Applications 389 (2010), no. 20, 4229 - 4254, Proceedings of the 12th International Summer School on Fundamental Problems in Statistical Physics - http://arxiv.org/abs/0911.2765
- Y. V. Fyodorov and J.-P. Bouchaud, Freezing and extreme-value statistics in a random energy model with logarithmically correlated potential, J. Phys. A 41 (2008), no. 37, 372001, 12 - http://www.ams.org/mathscinet-getitem?mr=2430565
- Y. V. Fyodorov and J. P. Keating, Freezing transitions and extreme values: Random matrix theory, ?(1/2 + it), and disordered landscapes, preprint - http://arxiv.org/abs/1211.6063
- Y. V. Fyodorov, P. Le Doussal, and A. Rosso, Statistical mechanics of logarithmic REM: duality, freezing and extreme value statistics of 1/f noises generated by Gaussian free fields, J. Stat. Mech. Theory Exp. (2009), no. 10, P10005, 32 - http://www.ams.org/mathscinet-getitem?mr=2882779
- Y. V. Fyodorov, P. Le Doussal, Counting function fluctuations and extreme value threshold in multifractal patterns: the case study of an ideal 1/f noise, J. Stat. Phys. 149 (2012), no. 5, 898-920 - http://www.ams.org/mathscinet-getitem?mr=2999566
- E. J. Gumbel, The distribution of the range, Ann. Math. Statistics 18 (1947), 384-412 - http://www.ams.org/mathscinet-getitem?mr=0022331
- J.-P. Kahane, Sur le chaos multiplicatif, Ann. Sci. Math. Québec 9 (1985), no. 2, 105-150 - http://www.ams.org/mathscinet-getitem?mr=829798
- O. Kallenberg, Random measures, third ed., Akademie-Verlag, Berlin, 1983 - http://www.ams.org/mathscinet-getitem?mr=818219
- O. Kallenberg, Foundations of modern probability, second ed., Probability and its Applications (New York), Springer-Verlag, New York, 2002 - http://www.ams.org/mathscinet-getitem?mr=1876169
- S. P. Lalley and T. Sellke, A conditional limit theorem for the frontier of a branching Brownian motion, Ann. Probab. 15 (1987), no. 3, 1052-1061 - http://www.ams.org/mathscinet-getitem?mr=893913
- T. Madaule, Convergence in law for the branching random walk seen from its tip, preprint - http://arxiv.org/abs/1107.2543
- T. Madaule, Maximum of a log-correlated gaussian field, preprint - http://arxiv.org/abs/1307.1365
- T. Madaule, R. Rhodes, and V. Vargas, Glassy phase and freezing of log-correlated gaussian potentials, preprint - http://arxiv.org/abs/1310.5574
- P. Maillard, A note on stable point processes occurring in branching Brownian motion, Elec-
tron. Commun. Probab. 18 (2013), no. 5, 9 - http://www.ams.org/mathscinet-getitem?mr=3019668 - H. P. McKean, Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov, Comm. Pure Appl. Math. 28 (1975), no. 3, 323-331 - http://www.ams.org/mathscinet-getitem?mr=0400428
- R. Rhodes and V. Vargas, Multidimensional multifractal random measures, Electron. J. Probab. 15 (2010), no. 9, 241-258 - http://www.ams.org/mathscinet-getitem?mr=2609587
- R. Rhodes and V. Vargas, Gaussian multiplicative chaos and applications: a review, preprint - http://arxiv.org/abs/1305.6221
- R. Robert and V. Vargas, Gaussian multiplicative chaos revisited, Ann. Probab. 38 (2010), no. 2, 605-631 - http://www.ams.org/mathscinet-getitem?mr=2642887
- S. Sheffield, Gaussian free fields for mathematicians, Probab. Theory Related Fields 139 (2007), no. 3-4, 521-541 - http://www.ams.org/mathscinet-getitem?mr=2322706
- Christian Webb, Exact asymptotics of the freezing transition of a logarithmically correlated random energy model, J. Stat. Phys. 145 (2011), no. 6, 1595-1619 - http://www.ams.org/mathscinet-getitem?mr=2863721
