Related papers: Weighted random staircase tableaux
A vector composition of a vector $\mathbf{\ell}$ is a matrix $\mathbf{A}$ whose rows sum to $\mathbf{\ell}$. We define a weighted vector composition as a vector composition in which the column values of $\mathbf{A}$ may appear in different…
Many enumeration problems in combinatorics, including such fundamental questions as the number of regular graphs, can be expressed as high-dimensional complex integrals. Motivated by the need for a systematic study of the asymptotic…
Tree-like tableaux are combinatorial objects that appear in a combinatorial understanding of the PASEP model from statistical mechanics. In this understanding, the corners of the Southeast border correspond to the locations where a particle…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
We introduce and study several random combinatorial billiard trajectories. Such a system, which depends on a fixed parameter $p\in(0,1)$, models a beam of light that travels in a Euclidean space, occasionally randomly reflecting off of a…
Covariate balance is crucial for unconfounded descriptive or causal comparisons. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of…
Covariate balance is crucial for unconfounded descriptive or causal comparisons. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of…
In this paper we consider a model of particles jumping on a row of cells, called in physics the one dimensional totally asymmetric exclusion process (TASEP). More precisely we deal with the TASEP with open or periodic boundary conditions…
The asymptotic distribution of the likelihood-ratio statistic for testing parameters on the boundary is well known to be a chi-squared mixture. The mixture weights have been shown to correspond to the intrinsic volumes of an associated…
We study a two-species PASEP, in which there are two types of particles, "heavy" and "light," hopping right and left on a one-dimensional lattice of $n$ cells with open boundaries. In this process, only the "heavy" particles can enter on…
We study asymptotics of random shifted Young diagrams which correspond to a given sequence of reducible projective representations of the symmetric groups. We show limit results (Law of Large Numbers and Central Limit Theorem) for their…
We develop a unified construction of matrix-valued orthogonal polynomials associated with discrete weights, yielding bispectral sequences as eigenfunctions of second-order difference operators. This general framework extends the discrete…
Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen at random with probability proportional to its weight. In the case where the total…
We investigate pattern avoidance in alternating permutations and generalizations thereof. First, we study pattern avoidance in an alternating analogue of Young diagrams. In particular, we extend Babson-West's notion of shape-Wilf…
This paper will be devoted to study weighted (deformed) free Poisson random variables from the viewpoint of orthogonal polynomials and statistics of non-crossing partitions. A family of weighted (deformed) free Poisson random variables will…
This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
In this paper we investigate the geometry of a discrete Bayesian network whose graph is a tree all of whose variables are binary and the only observed variables are those labeling its leaves. We provide the full geometric description of…
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…
The purpose of this note is to give an exposition of some interesting combinatorics and convex geometry concepts that appear in algebraic geometry in relation to counting the number of solutions of a system of polynomial equations in…