相关论文: On the correlation of the Moebius function with ra…

The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study…

We study, in the context of algorithmic randomness, the closed amenable subgroups of the symmetric group $S_\infty$ of a countable set. In this paper we address this problem by investigating a link between the symmetries associated with…

In this work, we aim to study a strong version of Ito's lemma for convex function. By considering the corresponding sub-martingale on a Brownian motion, we gain more insights about the convex function through a probabilistic viewpoint. The…

We fully describe the general form of a linear (or conjugate-linear) rank metric isometry on the Murray--von Neumann algebra associated with a II$_1$-factor. As an application, we establish Frobenius' theorem in the setting of…

This paper shows the existence of independent random matching of a large (continuum) population in both static and dynamic systems, which has been popular in the economics and genetics literatures. We construct a joint agent-probability…

We prove a convergence result for a large class of random models that encompasses the case of the BPHZ models used in the study of singular stochastic PDEs. We introduce for that purpose a useful variation on the notion of regularity…

We introduce a general class of statistical-mechanics models, taking values in an abelian group, which includes examples of both spin and gauge models, both ordered and disordered. The model is described by a set of ``variables'' and a set…

We consider the problem of counting the number of possible sets of rankings (called ranking patterns) generated by unfolding models of codimension one. We express the ranking patterns as slices of the braid arrangement and show that all…

We explore the link between combinatorics and probability generated by the question "What does a random parking function look like?" This gives rise to novel probabilistic interpretations of some elegant, known generating functions. It…

An inequality for the variance of an additive function defined on random decomposable structures, called assemblies, is established. The result generalizes estimates obtained earlier in the cases of permutations and mappings of a finite set…

Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…

We consider Poissonian pair correlations (PPC) for uniformly distributed sequences of random numbers with a dependency structure. More specifically, we treat two classes of dependent random variables which have widely been studied in the…

We investigate the effect of randomness in both relationships and decisions on the evolution of cooperation. Simulation results show, in such randomness' presence, the system evolves to a more frequency cooperation state than in its…

The purpose of modeling document relevance for search engines is to rank better in subsequent searches. Document-specific historical click-through rates can be important features in a dynamic ranking system which updates as we accumulate…

Given an orthogonal polynomial sequence on the real line, another sequence of polynomials can be found by composing these polynomials with a general M\"obius transformation. In this work, we study the properties of such M\"obius-transformed…

We study the problem of detecting a drift change of a Brownian motion under various extensions of the classical case. Specifically, we consider the case of a random post-change drift and examine monotonicity properties of the solution with…

It is shown that Sarnak's M\"{o}bius orthogonality conjecture is fulfilled for the compact metric dynamical systems for which every invariant measure has singular spectra. This is accomplished by first establishing a special case of Chowla…

The interest in orthogonal polynomials and random Fourier series in numerous branches of science and a few studies on random Fourier series in orthogonal polynomials inspired us to focus on random Fourier series in Jacobi polynomials. In…

We analyze the mixing properties of growing networks and find that, in some cases, the assortativity patterns are reversed once links' direction is considered: the disassortative behavior observed in such networks is a spurious effect, and…

For any given Cuntz semigroup, we introduce a function associated to it, called the ``Rank Ratio Function". This function ensures global control over the oscillation of the rank of any pair of elements in the Cuntz semigroup and, also,…