Related papers: Limit shapes for Gibbs ensembles of partitions

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 canonical Gibbs ensembles of partitions of sets,…

We compute the limit shape for several classes of restricted integer partitions, where the restrictions are placed on the part sizes rather than the multiplicities. Our approach utilizes certain classes of bijections which map limit shapes…

We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, $a_k\sim Ck^{p-1}, k\to\infty, p>0$,where $C$ is a positive constant. The measures…

We study random composite structures considered up to symmetry that are sampled according to weights on the inner and outer structures. This model may be viewed as an unlabelled version of Gibbs partitions and encompasses multisets of…

We study Gibbs partitions that typically form a unique giant component. The remainder is shown to converge in total variation toward a Boltzmann-distributed limit structure. We demon- strate how this setting encompasses arbitrary weighted…

For a subfamily of multiplicative measures on integer partitions we give conditions for properly rescaled associated Young diagrams to converge in probability to a certain deterministic curve named the limit shape of partitions. We provide…

After a quick review of the representation theory of the symmetric group, we give an exposition of the tools brought about by the so-called half-infinite wedge representation of the infinite symmetric group. We show how these can be applied…

According to the Quantum de Finetti Theorem, locally normal infinite particle states with Bose-Einstein symmetry can be represented as mixtures of infinite tensor powers of vector states. This note presents examples of infinite-particle…

We derive the limit shape of Young diagrams, associated with growing integer partitions, with respect to multiplicative probability measures underpinned by the generating functions of the form $\mathcal{F}(z)=\prod_{\ell=1}^\infty…

We investigate, in a fairly general setting, the limit of large volume equilibrium Gibbs measures for elasticity type Hamiltonians with clamped boundary conditions. The existence of a quasiconvex free energy, forming the large deviations…

We consider a system of classical particles confined in a box $\Lambda\subset\mathbb{R}^d$ with zero boundary conditions interacting via a stable and regular pair potential. Based on the validity of the cluster expansion for the canonical…

For a class of random partitions of an infinite set a de Finetti-type representation is derived, and in one special case a central limit theorem for the number of blocks is shown.

Gibbs random fields corresponding to systems of real-valued spins (e.g. systems of interacting anharmonic oscillators) indexed by the vertices of unbounded degree graphs with a certain summability property are constructed. It is proven that…

Genetic and evolution algebras arise naturally from applied probability and stochastic processes. Gibbs measures describe interacting systems commonly studied in thermodynamics and statistical mechanics with applications in several fields.…

We prove asymptotic 0-1 Laws satisfied by diagrams of unimodal sequences of positive integers. These diagrams consist of columns of squares in the plane, and the upper boundary is called the shape. For various types, we show that, as the…

This is an expository note answering a question posed to us by Richard Stanley, in which we prove a limit shape theorem for partitions of $n$ which maximize the number of subpartitions. The limit shape and the growth rate of the number of…

We establish necessary and sufficient conditions for convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. We show that this convergence is equivalent to asymptotic independence…

Gibbs-type exchangeable random partitions, which is a class of multiplicative measures on the set of positive integer partitions, appear in various contexts, including Bayesian statistics, random combinatorial structures, and stochastic…

We consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of…

We show that the Wigner equations describing the continuous spin representations can be obtained as a limit of massive higher-spin field equations. The limit involves a suitable scaling of the wave function, the mass going to zero and the…