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Abstract:

Zero-range processes with jump rates that decrease with the number of particles per site can exhibit a condensation transition, where a positive fraction of all particles condenses on a single site when the total density exceeds a critical value. We consider rates which decay as a power law or a stretched exponential to a non-zero limiting value, and study the onset of condensation at the critical density. We establish a law of large numbers for the excess mass fraction in the maximum, as well as distributional limits for the fluctuations of the maximum and the fluctuations in the bulk. © 2013 Elsevier B.V. All rights reserved.

Registro:

Documento: Artículo
Título:Zero-range condensation at criticality
Autor:Armendáriz, I.; Grosskinsky, S.; Loulakis, M.
Filiación:Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, C1428EGA, Buenos Aires, Argentina
Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom
School of Applied Mathematical and Physical Sciences, National Technical University of Athens, 15780 Athens, Greece
Institute of Applied and Computational Mathematics, FORTH, Heraklion Crete, Greece
Palabras clave:Condensation; Conditional maximum; Subexponential tails; Zero-range process; Condensation transition; Conditional maximum; Critical density; Law of large numbers; Limiting values; Stretched exponential; Subexponential tails; Zero-range process; Computer simulation; Statistics; Stochastic systems; Condensation
Año:2013
Volumen:123
Número:9
Página de inicio:3466
Página de fin:3496
DOI: http://dx.doi.org/10.1016/j.spa.2013.04.021
Título revista:Stochastic Processes and their Applications
Título revista abreviado:Stoch. Processes Appl.
ISSN:03044149
CODEN:STOPB
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_03044149_v123_n9_p3466_Armendariz.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03044149_v123_n9_p3466_Armendariz

Referencias:

  • Andjel, E.D., Invariant measures for the zero range process (1982) Ann. Probab., 10 (3), pp. 525-547
  • Andjel, E.D., Ferrari, P.A., Guiol, H., Landim, C., Convergence to the maximal invariant measure for a zero-range process with random rates (2000) Stochastic Process. Appl., 90, pp. 67-81
  • Armendáriz, I., Loulakis, M., Thermodynamic limit for the invariant measures in supercritical zero range processes (2009) Probab. Theory Related Fields, 145 (12), pp. 175-188
  • Armendáriz, I., Loulakis, M., Conditional distribution of heavy tailed random variables on large deviations of their sum (2011) Stochastic Process. Appl., 121 (5), pp. 1138-1147
  • Beltrán, J., Landim, C., Tunneling and metastability of continuous time Markov Chains (2010) J. Stat. Phys., 140 (6), pp. 1065-1114
  • Beltrán, J., Landim, C., Metastability of reversible condensed zero range processes on a finite set (2011) Probab. Theory Related Fields, , 10.1007/s00440-010-0337-0
  • Billingsley, P., (1968) Convergence of Probability Measures, , first ed. John Wiley New York
  • Biskup, M., Chayes, L., Kotecký, R., On the formation/dissolution of equilibrium droplets (2002) Europhys. Lett., 60 (1), pp. 21-27
  • Biskup, M., Chayes, L., Kotecky, R., Critical Region for Droplet Formation in the Two-Dimensional Ising Model (2003) Communications in Mathematical Physics, 242 (1-2), pp. 137-183
  • Chleboun, P., Grosskinsky, S., Finite size effects and metastability in zero-range condensation (2010) J. Stat. Phys., 140 (5), pp. 846-872
  • Davis, B., McDonald, D., An elementary proof of the local central limit theorem (1995) J. Theoret. Probab., 8 (3), pp. 693-701
  • Denisov, D., Dieker, A.B., Shneer, V., Large deviations for random walks under subexponentiality: The big-jump domain (2008) Ann. Probab., 36, pp. 1946-1991
  • Doney, R.A., A local limit theorem for moderate deviations (2001) Bulletin of the London Mathematical Society, 33 (1), pp. 100-108
  • Evans, M.R., Phase transitions in one-dimensional nonequilibrium systems (2000) Braz. J. Phys., 30 (1), pp. 42-57
  • Evans, M.R., Hanney, T., Nonequilibrium statistical mechanics of the zero-range process and related models (2005) J. Phys. A: Math. Gen., 38, pp. 195-R240
  • Evans, M.R., Majumdar, S.N., Condensation and extreme value statistics (2008) J. Stat. Mech., p. 05004
  • Ferrari, P., Landim, C., Sisko, V., Condensation for a fixed number of independent random variables (2007) J. Stat. Phys., 128 (5), pp. 1153-1158
  • Ferrari, P.A., Sisko, V., Escape of mass in zero-range processes with random rates (2007) IMS Lecture Notes Asymptotics: Particles, Processes and Inverse Problems, 55 VOL., pp. 108-120
  • Gnedenko, B.V., Kolmogorov, A.N., (1968) Limit Distributions for Sums of Independent Random Variables, , Addison-Wesley London
  • Großkinsky, S., Equivalence of ensembles for two-species zero-range invariant measures (2008) Stochastic Process. Appl., 118 (8), pp. 1322-1350
  • Grosskinsky, S., Schutz, G.M., Spohn, H., Condensation in the Zero Range Process: Stationary and Dynamical Properties (2003) Journal of Statistical Physics, 113 (3-4), pp. 389-410. , DOI 10.1023/A:1026008532442
  • Jeon, I., March, P., Pittel, B., Size of the largest cluster under zero-range invariant measures (2000) Annals of Probability, 28 (3), pp. 1162-1194. , DOI 10.1214/aop/1019160330
  • Kipnis, C., Landim, C., Scaling limits of interacting particle systems (1999) Grundlehren der Mathematischen Wissenschaften, 320 VOL.. , Springer Verlag Berlin
  • Landim, C., Hydrodynamic limit for space inhomogeneous one-dimensional totally asymmetric zero-range processes (1996) Ann. Probab., 24 (2), pp. 599-638
  • Nagaev, A.V., Local limit theorems with regard to large deviations when Cramér's condition is not satisfied (1968) Litovsk. Mat. Sb., 8, pp. 553-579
  • Spitzer, F., Interaction of Markov processes (1970) Adv. Math., 5, pp. 246-290

Citas:

---------- APA ----------
Armendáriz, I., Grosskinsky, S. & Loulakis, M. (2013) . Zero-range condensation at criticality. Stochastic Processes and their Applications, 123(9), 3466-3496.
http://dx.doi.org/10.1016/j.spa.2013.04.021
---------- CHICAGO ----------
Armendáriz, I., Grosskinsky, S., Loulakis, M. "Zero-range condensation at criticality" . Stochastic Processes and their Applications 123, no. 9 (2013) : 3466-3496.
http://dx.doi.org/10.1016/j.spa.2013.04.021
---------- MLA ----------
Armendáriz, I., Grosskinsky, S., Loulakis, M. "Zero-range condensation at criticality" . Stochastic Processes and their Applications, vol. 123, no. 9, 2013, pp. 3466-3496.
http://dx.doi.org/10.1016/j.spa.2013.04.021
---------- VANCOUVER ----------
Armendáriz, I., Grosskinsky, S., Loulakis, M. Zero-range condensation at criticality. Stoch. Processes Appl. 2013;123(9):3466-3496.
http://dx.doi.org/10.1016/j.spa.2013.04.021