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.
On averages of randomized class functions on the symmetric groups and their asymptotics
The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices ( points). In this paper, we generalize many aspects of this situation. We introduce random shifts of the eigenvalues of the permutation matrices, in two different ways: independently or not for each subset of eigenvalues associated to the same cycle. We also consider vastly more general functions than the characteristic polynomial of a permutation matrix, by...
On certain combinatorial identities
On concentration of self-bounding functions.
On coverings of random graphs
On exchangeable random variables and the statistics of large graphs and hypergraphs.
On families of weakly dependent random variables
Let be a family of random independent k-element subsets of [n] = 1,2,...,n and let denote a family of ℓ-element subsets of [n] such that the event that S belongs to depends only on the edges of contained in S. Then, the edges of are ’weakly dependent’, say, the events that two given subsets S and T are in are independent for vast majority of pairs S and T. In the paper we present some results on the structure of weakly dependent families of subsets obtained in this way. We also list...
On lattice path counting by major and descents.
On logic transformations of the binary stochastic process
On pendant vertices in random graphs
On percolation in random graphs with given vertex degrees.
On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications
On Q-independence, limit theorems and q-Gaussian distribution
We formulate the notion of Q-independence which generalizes the classical independence of random variables and free independence introduced by Voiculescu. Here Q stands for a family of polynomials indexed by tiny partitions of finite sets. The analogs of the central limit theorem and Poisson limit theorem are proved. Moreover, it is shown that in some special cases this kind of independence leads to the q-probability theory of Bożejko and Speicher.
On randomly colouring locally sparse graphs.
On Sets of Integers with Prescribed Gaps.
On some densities in the set of permutations.