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Abstract
We study the factorized steady state of a general class of mass transport models in which mass, a conserved quantity, is transferred stochastically between sites. Condensation in such models is exhibited when above a critical mass density the marginal distribution for the mass at a single site develops a bump, p(cond)(m), at large mass m. This bump corresponds to a condensate site carrying a finite fraction of the mass in the system. Here, we study the condensation transition from a different aspect, that of extreme value statistics. We consider the cumulative distribution of the largest mass in the system and compute its asymptotic behaviour. We show three distinct behaviours: at subcritical densities the distribution is Gumbel; at the critical density the distribution is Frechet, and above the critical density a different distribution emerges. We relate p(cond)(m) to the probability density of the largest mass in the system.
Original language  English 

Article number  P05004 
Pages (fromto)   
Number of pages  11 
Journal  Journal of Statistical Mechanics: Theory and Experiment 
DOIs  
Publication status  Published  May 2008 
Keywords
 stochastic particle dynamics (theory)
 stationary states
 zerorange processes
 large deviations in nonequilibrium systems
 FACTORIZED STEADYSTATES
 MASSTRANSPORT MODELS
 ZERORANGE PROCESSES
 PHASETRANSITIONS
 PARTICLESYSTEMS
 RANDOM MATRICES
 FLUCTUATIONS
 AGGREGATION
 EIGENVALUE
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Dive into the research topics of 'Condensation and extreme value statistics'. Together they form a unique fingerprint.Projects
 1 Finished

Edinbugrh Soft Matter and Statistical Physics Programme Grant Renewal
Cates, M., Poon, W., Ackland, G., Clegg, P., Evans, M., MacPhee, C. & Marenduzzo, D.
1/10/07 → 31/03/12
Project: Research