Maximal arithmetic progressions in random subsets.
Mean mutual information and symmetry breaking for finite random fields
G. Edelman, O. Sporns and G. Tononi have introduced the neural complexity of a family of random variables, defining it as a specific average of mutual information over subfamilies. We show that their choice of weights satisfies two natural properties, namely invariance under permutations and additivity, and we call any functional satisfying these two properties an intricacy. We classify all intricacies in terms of probability laws on the unit interval and study the growth rate of maximal intricacies...
min-wise independent linear permutations.
Mixing time for a random walk on rooted trees.
Mixing time of the Rudvalis shuffle.
Mixture decompositions of exponential families using a decomposition of their sample spaces
We study the problem of finding the smallest such that every element of an exponential family can be written as a mixture of elements of another exponential family. We propose an approach based on coverings and packings of the face lattice of the corresponding convex support polytopes and results from coding theory. We show that is the smallest number for which any distribution of
Monotonic subsequences in dimensions higher than one.
Multiplicative free square of the free Poisson measure and examples of free symmetrization
We compute the moments and free cumulants of the measure , where denotes the free Poisson law with parameter t > 0. We also compute free cumulants of the symmetrization of . Finally, we introduce the free symmetrization of a probability measure on ℝ and provide some examples.
Multiplicative functions on the lattice of non-crossing partitions and free convolution.
Neighborliness of marginal polytopes.
Noise sensitivity of boolean functions and applications to percolation
Normal approximation for isolated balls in an urn allocation model.
Note: random-to-front shuffles on trees.
Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws.
Number theory, balls in boxes, and the asymptotic uniqueness of maximal discrete order statistics.
O jistém problému z počtu pravděpodobnosti
Observations de M. Rouché en réponse à une Note de M. Delannoy
Odd cutsets and the hard-core model on
We consider the hard-core lattice gas model on and investigate its phase structure in high dimensions. We prove that when the intensity parameter exceeds , the model exhibits multiple hard-core measures, thus improving the previous bound of given by Galvin and Kahn. At the heart of our approach lies the study of a certain class of edge cutsets in , the so-called odd cutsets, that appear naturally as the boundary between different phases in the hard-core model. We provide a refined combinatorial...
On a sphere of influence graph in a one-dimensional space
A sphere of influence graph generated by a finite population of generated points on the real line by a Poisson process is considered. We determine the expected number and variance of societies formed by population of n points in a one-dimensional space.
On a uniformly integrable family of polynomials defined on the unit interval.