Canonical Analysis of Condensation in Factorised Steady States

Evans, Martin R.; Majumdar, Satya N.; Zia, R. K. P.

doi:10.1007/s10955-006-9046-6

Cited by 115 publications

(267 citation statements)

References 49 publications

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“…In the condensed phase this distribution has a bump around the excess mass M − ρ c L as computed in [13,14]. More rigorous work on standard condensation can be found in [15][16][17].…”

Section: Introductionmentioning

confidence: 80%

See 1 more Smart Citation

Condensation transition in joint large deviations of linear statistics

Szavits-Nossan¹,

Evans²,

Majumdar³

2014

J. Phys. A: Math. Theor.

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Abstract. Real space condensation is known to occur in stochastic models of mass transport in the regime in which the globally conserved mass density is greater than a critical value. It has been shown within models with factorised stationary states that the condensation can be understood in terms of sums of independent and identically distributed random variables: these exhibit condensation when they are conditioned to a large deviation of their sum. It is well understood that the condensation, whereby one of the random variables contributes a finite fraction to the sum, occurs only if the underlying probability distribution (modulo exponential) is heavy-tailed, i.e. decaying slower than exponential. Here we study a similar phenomenon in which condensation is exhibited for non-heavy-tailed distributions, provided random variables are additionally conditioned on a large deviation of certain linear statistics. We provide a detailed theoretical analysis explaining the phenomenon, which is supported by Monte Carlo simulations (for the case where the additional constraint is the sample variance) and demonstrated in several physical systems. Our results suggest that the condensation is a generic phenomenon that pertains to both typical and rare events.

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“…In the condensed phase this distribution has a bump around the excess mass M − ρ c L as computed in [13,14]. More rigorous work on standard condensation can be found in [15][16][17].…”

Section: Introductionmentioning

confidence: 80%

“…Recently it has been appreciated that the condensation phenomenon, at least in the context of factorised stationary states, is related to large deviations of sums of random variables [13][14][15][16]. To see this we consider the normalisation in (1)…”

Section: Introductionmentioning

confidence: 99%

Condensation transition in joint large deviations of linear statistics

Szavits-Nossan¹,

Evans²,

Majumdar³

2014

J. Phys. A: Math. Theor.

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“…For the single condensate case, in [10,11] the condensate peak, denoted p cond (n) in that work, has been computed. The scaling form of the peak is as follows: the position scales as n * ∼ L; the width scales as n * ∼ L The peak is sharp, as in the case we have studied of a finite number of condensates.…”

Section: Discussionmentioning

confidence: 99%

Zero-range processes with multiple condensates: statics and dynamics

Schwarzkopf¹,

Evans²,

Mukamel³

2008

J. Phys. A: Math. Theor.

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The steady-state distributions and dynamical behaviour of zero-range processes with hopping rates which are non-monotonic functions of the site occupation are studied. We consider two classes of non-monotonic hopping rates. The first results in a condensed phase containing a large (but subextensive) number of mesocondensates each containing a subextensive number of particles. The second results in a condensed phase containing a finite number of extensive condensates. We study the scaling behaviour of the peak in the distribution function corresponding to the condensates in both cases. In studying the dynamics of the condensate we identify two timescales: one for creation, the other for evaporation of condensates at a given site. The scaling behaviour of these timescales is studied within the Arrhenius law approach and by numerical simulations.

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“…Let the condensate be the site with the maximal occupancy. Precise estimates on the number of particles at the condensated, as well as its fluctuations, have been obtained in [9,8,5]. The equivalence of ensembles has been proved by Großkinsky, Schütz and Spohn [8].…”

Section: Introductionmentioning

confidence: 99%

Metastability of reversible condensed zero range processes on a finite set

Beltrán

Landim

2011

Probab. Theory Relat. Fields

158

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Abstract. Let r : S × S → R + be the jump rates of an irreducible random walk on a finite set S, reversible with respect to some probability measure m.Consider a zero range process on S in which a particle jumps from a site x, occupied by k particles, to a site y at rate g(k)r(x, y). Let N stand for the total number of particles. In the stationary state, as N ↑ ∞, all particles but a finite number accumulate on one single site. We show in this article that in the time scale N 1+α the site which concentrates almost all particles evolves as a random walk on S whose transition rates are proportional to the capacities of the underlying random walk.

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Canonical Analysis of Condensation in Factorised Steady States

Cited by 115 publications

References 49 publications

Condensation transition in joint large deviations of linear statistics

Condensation transition in joint large deviations of linear statistics

Zero-range processes with multiple condensates: statics and dynamics

Metastability of reversible condensed zero range processes on a finite set

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