Limit Shapes for Gibbs Ensembles of Partitions

  title={Limit Shapes for Gibbs Ensembles of Partitions},
  author={Ibrahim Fatkullin and Valeriy V. Slastikov},
  journal={Journal of Statistical Physics},
We explicitly compute limit shapes for several grand canonical Gibbs ensembles of partitions of integers. These ensembles appear in models of aggregation and are also related to invariant measures of zero range and coagulation-fragmentation processes. We show, that all possible limit shapes for these ensembles fall into several distinct classes determined by the asymptotics of the internal energies of aggregates. 
Limit Shapes for Gibbs Partitions of Sets
This study extends a prior investigation of limit shapes for partitions of integers, which was based on analysis of sums of geometric random variables. Here we compute limit shapes for grand
On hydrodynamic limits of Young diagrams
We consider a family of stochastic models of evolving two-dimensional Young diagrams, given in terms of certain energies, with Gibbs invariant measures. `Static' scaling limits of the shape
Large deviations analysis for random combinatorial partitions with counter terms
In this paper, we study various models for random combinatorial partitions using large deviation analysis for diverging scale of the reference process. The large deviation rate functions are
A Complete Bibliography of the Journal of Statistical Physics: 2000{2009
(2 + 1) [XTpXpH12, CTH11]. + [Zuc11b]. 0 [Fed17]. 1 [BELP15, CAS11, Cor16, Fed17, GDL10, GBL16, Hau16, JV19, KT12, KM19c, Li19, MN14b, Nak17, Pal11, Pan14, RT14, RBS16b, RY12, SS18c, Sug10, dOP18]. 1


Random partitions in statistical mechanics
We consider a family of distributions on spatial random partitions that provide a coupling between different models of interest: the ideal Bose gas; the zero-range process; particle clustering; and
Asymptotics of random partitions of a set
This paper contains two results on the asymptotic behavior of uniform probability measure on partitions of a finite set as its cardinality tends to infinity. The first one states that there exists a
Combinatorial Stochastic Processes
Preliminaries.- Bell polynomials, composite structures and Gibbs partitions.- Exchangeable random partitions.- Sequential constructions of random partitions.- Poisson constructions of random
The limit shape of random permutations with polynomially growing cycle weights
In this work we are considering the behaviour of the limit shape of Young diagrams associated to random permutations on the set {1, . . . , n} under a particular class of multiplicative measures with
Hydrodynamic Limit for an Evolutional Model of Two-Dimensional Young Diagrams
We construct dynamics of two-dimensional Young diagrams, which are naturally associated with their grandcanonical ensembles, by allowing the creation and annihilation of unit squares located at the
Asymptotics of Plancherel measures for symmetric groups
1.1. Plancherel measures. Given a finite group G, by the corresponding Plancherel measure we mean the probability measure on the set G∧ of irreducible representations of G which assigns to a
Limit shapes of Gibbs distributions on the set of integer partitions: The expansive case
Nous trouvons des formes limites pour une famille de mesures multiplicatives sur l’ensemble des partitions, induites par des fonctions generatrices exponentielles avec des parametres d’expansion
Fluctuations of the Bose–Einstein condensate
This paper gives a rigorous analysis of the fluctuations of the Bose–Einstein condensate for a system of non-interacting bosons in an arbitrary potential, assuming that the system is governed by the
Developments in the Khintchine-Meinardus Probabilistic Method for Asymptotic Enumeration
The asymptotics of Gentile statistics are proved rigorously and the hypotheses of the theorem are reformulated in terms of the above generating functions, which allows novel applications of the method.
Random partitions in population genetics
  • J. Kingman
  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1978
This characterization explains the robustness of the Ewens formula when neither selection nor recurrent mutation is significant, although different structures arise from selective and ‘charge-state’ models.