相关论文: Correlations of multiplicative functions along det…

By using a combination of algebraic, geometric, and dynamical techniques, together with input from higher dimensional Diophantine approximation, we give a complete characterization of all linearly repetitive cut and project sets with…

The geometry of Arithmetic Random Waves has been extensively investigated in the last fifteen years, starting from the seminal papers [RW08, ORW08]. In this paper we study the correlation structure among different functionals such as nodal…

A piecewise-deterministic Markov process, specified by random jumps and switching semi-flows, as well as the associated Markov chain given by its post-jump locations, are investigated in this paper. The existence of an exponentially…

Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…

We present a sequence-based probabilistic formalism that directly addresses co-operative effects in networks of interacting positions in proteins, providing significantly improved contact prediction, as well as accurate quantitative…

We consider two variables that are related to each other by an invertible function. While it has previously been shown that the dependence structure of the noise can provide hints to determine which of the two variables is the cause, we…

We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of…

We consider two Ito equations that evolve on different time scales. The equations are fully coupled in the sense that all coefficients may depend on both the "slow" and the "fast" processes and the diffusion terms may be correlated. The…

We form a sequence of oblong matrices by evaluating an integrable vector-valued function along the orbit of an ergodic dynamical system. We obtain an almost sure asymptotic result for the permanents of those matrices. We also give an…

We prove a Green--Tao theorem for multiplicative functions.

The analysis of extremal dependence in high dimensions has recently attracted considerable interest. Existing methodology primarily focuses on modeling and estimation of extremal dependence structures, often supported by concentration…

We introduce a class of multiplicative functions in which each function satisfies some statistic conditions, and then prove that above functions are not correlated with finite degree polynomial nilsequences. Besides, we give two…

Exploiting the equidistribution properties of polynomial sequences, following the methods developed by Leibman ("Pointwise Convergence of ergodic averages for polynomial sequences of translations on a nilmanifold. Ergodic Theory Dynam.…

The use of empirical characteristic functions for inference problems, including estimation in some special parametric settings and testing for goodness of fit, has a long history dating back to the 70s (see for example, Feuerverger and…

We study multiple ergodic averages along IP sets, meaning we restrict iterates in the averages to all finite sums of some infinite sequence of natural numbers. We give criteria for convergence and divergence in mean of these multiple…

We prove that given a measure preserving system $(X,\mathcal{B},\mu,T_1,\dots,T_d)$ with commuting, ergodic transformations $T_i$ such that $T_iT_j^{-1}$ are ergodic for all $i \neq j$, the multicorrelation sequence $a(n)=\int_X f_0 \cdot…

We investigate the limiting behavior of multiple ergodic averages along sparse sequences evaluated at prime numbers. Our sequences arise from smooth and well-behaved functions that have polynomial growth. Central to this topic is a…

In this paper, we prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share three sets. The obtained results improve some recent existing results.

Time-dependent structures often appear in differential geometry, particularly in the study of non-autonomous differential equations on manifolds. One may study the geodesics associated with a time-dependent Riemannian metric by extremizing…

This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…