Boundary driven zero-range processes in random media

Journal of Statistical Physics

Volumn 128, Issue 6, 2007, Pages 1289-1305

  Pulkkinen, Otto ^a  

^a UNIVERSITY OF JYVÄSKYLÄ   (Finland)

Author keywords

Random media; Subordinator; Tagged particle; Zero range process

Indexed keywords

EID: 34548570069     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-007-9361-6     Document Type: Article

References (40)

1. Spitzer, F.: Interaction of Markov processes. Adv. Math. 5, 246-290 (1970)
2. Andjel, E.D.: Invariant measures for the zero-range process. Ann. Prob. 10, 525-547 (1982)
3. Kipnis, C., Landim, C.: Scaling limits of interacting particle systems. Springer, Berlin (1999)
4. Bertini, L., de Sole, A., Gabrielli, D., Jona-Lasinio, G., Landim, C.: Macroscopic fluctuation theory for non-equilibrium stationary states. J. Stat. Phys. 107, 635-675 (2002)
5. Evans, M.R., Hanney, T.: Nonequilibrium statistical mechanics of the zero-range process and related models. J. Phys. A: Math. Gen. 38, R195-R240 (2005)
6. Levine, E., Mukamel, D., Schütz, G.M.: Zero-Range process with open boundaries. J. Stat. Phys. 120, 759-778 (2005)
7. Evans, M.R.: Bose-Einstein condensation in disordered exclusion models and relation to traffic flow. Europhys. Lett. 36, 13-18 (1996)
8. Krug, J., Ferrari, P.A.: Phase transitions in driven diffusive systems with random rates. J. Phys. A: Math. Gen. 29, L465-L471 (1996)
9. Havlin, S., Ben-Avraham, D.: Diffusion in disordered media. Adv. Phys. 36, 695-798 (1987)
10. Hughes, B.D.: Random Walks and Random Environments, vol. 2: Random Environments. Oxford University Press, Oxford (1996)
11. Zeitouni, O.: Random walks in random environments. J. Phys. A: Math. Gen. 39, R433-R464 (2006)
12. Isichenko, M.B.: Percolation, statistical topography, and transport in random media. Rev. Mod. Phys. 64, 961-1043 (1992)
13. Kawazu, K., Kesten, H.: On birth and death processes in symmetric random environment. J. Stat. Phys. 37, 561-576 (1984)
14. Ferrari, P.: Limit theorems for tagged particles. Markov Process. Relat. Fields 2, 17-40 (1996)
15. Saada, E.: Processus de zéro-rangé avec particule marquée. Ann. Inst. H. Poincaré Probab. Stat. 26, 5-17 (1990)
16. Siri, P.: Asymptotic behaviour of a tagged particle in an inhomogeneous zero-range process. Stoch. Process. Appl. 77, 139-154 (1998)
17. Sethuraman, S.: On diffusivity of a tagged particle in asymmetric zero-range dynamics. Ann. Inst. H. Poincaré Probab. Stat. 43, 215-232 (2007)
18. Derrida, B., Lebowitz, J.L., Speer, E.R.: Large deviation of the density profile in the steady state of the open symmetric simple exclusion process. J. Stat. Phys. 107, 599-634 (2002)
19. Sato, K.: Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge (1999)
20. Ibragimov, I.A., Linnik, Yu.V.: Independent and stationary sequences of random variables. Wolters-Noordhoff, Groningen (1971)
21. Billingsley, P.: Convergence of probability measures. Wiley, New York (1968)
22. Gihman, I.I., Skorohod, A.V.: The theory of stochastic processes, I. Springer, Berlin (1974)
23. Skorohod, A.V.: Limit theorems for stochastic processes. Theory Probab. Appl. 1, 261-290 (1956)
24. Skorohod, A.V.: Limit theorems for stochastic processes with independent increments. Theory Probab. Appl. 2, 138-171 (1957)
25. Bertoin, J.: Lévy Processes. Cambridge University Press, Cambridge (1996)
26. Pitman, J.: Combinatorial Stochastic Processes: Ecole d'Eté de Probabilités de Saint-Flour XXXII, 2002. Springer, Berlin (2006)
27. Regazzini, E., Lijoi, A., Prünster, I.: Distributional results for means of normalized random measures with independent increments. Ann. Stat. 31, 560-585 (2003)
28. Gurland, J.: Inversion formulae for the distribution of ratios. Ann. Math. Stat. 19, 228-237 (1948)
29. Perman, M., Pitman, J., Yor, M.: Size-biased sampling of Poisson point processes and excursions. Probab. Theory Related Fields 92, 21-39 (1992)
30. Pitman, J.: Some developments of the Blackwell-MacQueen urn scheme. In: Ferguson, T.S., Shapley, L.S., MacQueen, J.B. (eds.) Statistics, Probability and Game Theory; Papers in Honor of David Blackwell. Institute of Mathematical Statistics, Hayward (1996)
31. Pitman, J., Yor, M.: The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann. Probab. 25, 855-900 (1997)
32. Pitman, J.: Poisson-Kingman partitions. Technical Report No. 625, Department of Statistics, University of California, available via http://www.stat.berkeley.edu/tech-reports/
33. Talagrand, M.: Spin Glasses: a Challenge for Mathematicians. Springer, Berlin (2003)
34. Derrida, B.: Random-energy model: an exactly solvable model of disordered systems. Phys. Rev. B 24, 2613-2626 (1981)
35. Rogers, L.C.G., Williams, D.: Diffusions, Markov Processes and Martingales, vol. 2: Itô Calculus, 2nd edn. Cambridge University Press, Cambridge (2000)
36. Revuz, D., Yor, M.: Continuous Martingales and Brownian Motion, 3rd edn. Springer, Berlin (1999)
37. Kook, K., Serfozo, R.: Travel and sojourn times in stochastic networks. Ann. Appl. Probab. 3, 228-252 (1993)
38. Baccelli, F., Brémaud, P.: Elements of Queuing Theory, 2nd edn. Springer, Berlin (2003)
39. Whit, W.: A review of L=λ W and extensions. Queuing Syst. 9, 235-268 (1990)
40. Serfozo, R.: Introduction to Stochastic Networks. Springer, New York (1999)