Related papers: Unlabelled Gibbs partitions
This article considers a class of disordered mean-field combinatorial optimization problems. We focus on the Gibbs measure, where the inverse temperature does not vary with the size of the graph and the edge weights are sampled from a…
We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order…
We give an asymptotic estimate for the number of partitions of a set of $n$ elements, whose block sizes avoid a given set $\mathcal{S}$ of natural numbers. As an application, we derive an estimate for the number of partitions of a set with…
A random vector whose norm and overlap (inner product with an independent copy) concentrates is shown to have random low-dimensional projections that are approximately random Gaussians. Conversely, asymptotically random Gaussian projections…
We show that a Gibbs characterization of normalized generalized Gamma processes, recently obtained in Lijoi, Pr\"unster and Walker (2007), can alternatively be derived by exploiting a characterization of exponentially tilted Poisson-Kingman…
We consider procedures of sampling parts from a random integer partition. We determine asymptotically the probabilty distribution of the randomly-selected part whenever the positive integer that is partitioned becomes large.
Experimentally the existence of a light 125 GeV Higgs boson is well established but so far no other heavier resonances have been observed. Viable models to describe the Higgs boson as composite particle require hence to exhibit a large…
We consider a linear Hamiltonian system consisting of a classical particle and a scalar field describing by the wave or Klein-Gordon equations with variable coefficients. The initial data of the system are supposed to be a random function…
Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus…
We compare three notions of genericity of separable metric structures. Our analysis provides a general model theoretic technique of showing that structures are generic in descriptive set theoretic (topological) sense and in measure…
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of…
We study fragmentation trees of Gibbs type. In the binary case, we identify the most general Gibbs-type fragmentation tree with Aldous' beta-splitting model, which has an extended parameter range $\beta>-2$ with respect to the ${\rm…
A new class of random composition structures (the ordered analog of Kingman's partition structures) is defined by a regenerative description of component sizes. Each regenerative composition structure is represented by a process of random…
This paper studies the distribution of the component spectrum of combinatorial structures such as uniform random forests, in which the classical generating function for the numbers of (irreducible) elements of the different sizes converges…
We discuss recent results of the replica approach to statistical mechanics of a single classical particle placed in a random N(>>1)-dimensional Gaussian landscape. The particular attention is paid to the case of landscapes with…
On basis of an algebraic analysis of symmetry breaking in general and the Higgs mechanism in the standard model of elementary particles we generalize the concept of symmetry breaking to systems with non-compact groups but not necessarily…
For two collections of nonnegative and suitably normalised weights $\W=(\W_j)$ and $\V=(\V_{n,k})$, a probability distribution on the set of partitions of the set $\{1,...,n\}$ is defined by assigning to a generic partition $\{A_j, j\leq…
We characterise the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence…
We introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights. This framework encompasses the particular case of uniform non-crossing…
We use a model whose rules were inspired by population genetics, the random capability growth model, to describe the statistical details observed in experiments of fragmentation of brittle platelike objects, and in particular the existence…