Free powers of the free Poisson measure
We compute moments of the measures , where ϖ denotes the free Poisson law, and ⊞ and ⊠ are the additive and multiplicative free convolutions. These moments are expressed in terms of the Fuss-Narayana numbers.
From shuffling cards to walking around the building: An introduction to modern Markov chain theory.
Fuss-Catalan numbers in noncommutative probability.
Generalization of waiting times model
Generalized distributions of order associated with success runs in Bernoulli trials.
Generating a random sink-free orientation in quadratic time.
Generating functions and the satisfiability threshold.
Geometric influences II: Correlation inequalities and noise sensitivity
In a recent paper, we presented a new definition of influences in product spaces of continuous distributions, and showed that analogues of the most fundamental results on discrete influences, such as the KKL theorem, hold for the new definition in Gaussian space. In this paper we prove Gaussian analogues of two of the central applications of influences: Talagrand’s lower bound on the correlation of increasing subsets of the discrete cube, and the Benjamini–Kalai–Schramm (BKS) noise sensitivity theorem....
Graph-based upper bounds for the probability of the union of events.
Harmonic functions on multiplicative graphs and interpolation polynomials.
Hierarchical models, marginal polytopes, and linear codes
In this paper, we explore a connection between binary hierarchical models, their marginal polytopes, and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with the property that their vertices form a linear code and give an algorithm that determines them.
Hoeffding spaces and Specht modules
It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.
Hoeffding spaces and Specht modules
It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.
How frequently is a system of 2-linear Boolean equations solvable?
Identitäten bei den Stirling-Zahlen 2.Art aus kombinatorischen Überlegungen beim Würfelspiel.
Improved inclusion-exclusion identities and inequalities based on a particular class of abstract tubes.
Inclusion-exclusion and network reliability.
Inclusion-exclusion redux.
Inequalities and limit theorems for random allocations
Random allocations of balls into boxes are considered. Properties of the number of boxes containing a fixed number of balls are studied. A moment inequality is obtained. A merge theorem with Poissonian accompanying laws is proved. It implies an almost sure limit theorem with a mixture of Poissonian laws as limiting distribution. Almost sure versions of the central limit theorem are obtained when the parameters are in the central domain.
Inequalities of Bonferroni-Galambos type with applications to the Tutte polynomial and the chromatic polynomial.