Related papers: Correlation inequalities for linear extensions

We give new bounds and asymptotic estimates on the number of standard Young tableaux of skew shape in a variety of special cases. Our approach is based on Naruse's hook-length formula. We also compare our bounds with the existing bounds on…

We use a recently proposed scheme of matrix extension of dispersionless integrable systems for the Abelian case, in which it leads to linear equations, connected with the initial dispersionless system. In the examples considered, these…

Some natural inequalities related to rearrangement in matrix products can also be regarded as extensions of classical inequalities for sequences or integrals. In particular, we show matrix versions of Chebyshev and Kantorovich type…

We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…

We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…

We determine the nonlinear transformations between coordinate systems which are mutually in a constant symmetrical accelerated motion. The maximal acceleration limit follows from the kinematical origin and it is an analogue of the maximal…

Statistical and scaling properties of the Lyapunov exponent for a tight-binding model with the diagonal disorder described by a dichotomic process are considered near the band edge. The effect of correlations on scaling properties is…

In the context of the Beckerian theory of marriage, when men and women match on a single-dimensional index that is the weighted sum of their respective multivariate attributes, many papers in the literature have used linear canonical…

We construct and analyze an estimator of association between random variables based on their similarity in both direction and magnitude. Under special conditions, the proposed measure becomes a robust and consistent estimator of the linear…

A variety of possible extensions of mappings between posets to their Dedekind order completion is presented. One of such extensions has recently been used for solving large classes of nonlinear systems of partial differential equations with…

Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…

Achieving the goals in the title (and others) relies on a cardinality-wise scanning of the ideals of the poset. Specifically, the relevant numbers attached to the k+1 element ideals are inferred from the corresponding numbers of the…

The divergence of the correlation length $\xi$ at criticality is an important phenomenon of percolation in two-dimensional systems. Substantial speed-ups to the calculation of the percolation threshold and component distribution have been…

We review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superposition rules, the Lewis-Ermakov invariants, etc., are found…

Time series regression models are commonly used in time series analysis. However, in modern real-world applications, serially correlated data with an ultra-high dimension and fat tails are prevalent. This presents a challenge in developing…

This paper develops some theory of the Dyson equation for correlated linearizations and uses it to solve a problem on asymptotic deterministic equivalent for the test error in random features regression. The theory developed for the…

The Kahn--Saks inequality is a classical result on the number of linear extensions of finite posets. We give a new proof of this inequality for posets of width two using explicit injections of lattice paths. As a consequence we obtain a…

We discuss counting problems linked to finite versions of Cantor's diagonal of infinite tableaux. We extend previous results of [2] by refining an equivalence relation that reduces significantly the exhaustive generation. New enumerative…

Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the…

For the formal verification and design of control systems, abstractions with quantified accuracy are crucial. This is especially the case when considering accurate deviation bounds between a stochastic continuous-state model and its finite…