Related papers: Correlation for permutations
We study a class of quantum measurement models. A microscopic object is entangled with a macroscopic pointer such that a distinct pointer position is tied to each eigenvalue of the measured object observable. Those different pointer…
Given a set $I \subseteq \mathbb{N}$, consider the sequences $\{d_n(I)\},\{p_n(I)\}$ where for any $n$, $d_n(I)$ and $p_n(I)$ respectively count the number of permutations in the symmetric group $\mathfrak{S}_n$ whose descent set…
The structure of order ideals in the Bruhat order for the symmetric group is elucidated via permutation patterns. A method for determining non-isomorphic principal order ideals is described and applied for small lengths. The permutations…
In theory of Coxeter groups, bigrassmannian elements are well known as elements which have precisely one left descent and precisely one right descent. In this article, we prove formulas on enumeration of bigrassmannian permutations weakly…
Vecchia's approximate likelihood for Gaussian process parameters depends on how the observations are ordered, which can be viewed as a deficiency because the exact likelihood is permutation-invariant. This article takes the alternative…
Temporal steering and violation of the Leggett-Garg inequality are two different ways of probing the violation of macro-realistic assumptions in quantum mechanics. It is shown here that under unitary evolution and projective measurements…
We establish a sprinkled decoupling inequality for increasing events of Gaussian vectors with an error that depends only on the maximum pairwise correlation. As an application we prove the non-triviality of the percolation phase transition…
It is well-known that in a Bell experiment, the observed correlation between measurement outcomes -- as predicted by quantum theory -- can be stronger than that allowed by local causality, yet not fully constrained by the principle of…
Gravitationally collapsed objects are known to be biased tracers of an underlying density contrast. Using symmetry arguments, generalised biasing schemes have recently been developed to relate the halo density contrast $\delta_h$ with the…
We study the existence, uniqueness and rate of decay of correlation of equilibrium measures associated to robust classes of non-uniformly expanding local diffeomorphisms and H\"older continuous potentials. The approach used in this paper is…
I discuss fluctuations in the neutral hydrogen (HI) density of the z~2.3 intergalactic medium and show that their relation to cosmic overdensity is strongly scale-dependent. This behaviour arises from a linearized version of the well-known…
In this study, we consider a variant of unlabelled sensing where the measurements are sparsely permuted, and additionally, a few correspondences are known. We present an estimator to solve for the unknown vector. We derive a theoretical…
Sampling permutations from S_n is a fundamental problem from probability theory. The nearest neighbor transposition chain \cal{M}}_{nn} is known to converge in time \Theta(n^3 \log n) in the uniform case and time \Theta(n^2) in the constant…
Let $S_n$ be the symmetric group on the set $\{1,2,\ldots,n\}$. Given a permutation $\sigma=\sigma_1\sigma_2 \cdots \sigma_n \in S_n$, we say it has a peak at index $i$ if $\sigma_{i-1}<\sigma_i>\sigma_{i+1}$. Let $\text{Peak}(\sigma)$ be…
In this paper, we study the uniform measure for the self-conjugate partitions. We derive the $q$-difference equation which is satisfied by the $n$-point correlation function related to the uniform measure. As applications, we give explicit…
The order $O_n(\sigma)$ of a permutation $\sigma$ of $n$ objects is the smallest integer $k \geq 1$ such that the $k$-th iterate of $\sigma$ gives the identity. A remarkable result about the order of a uniformly chosen permutation is due to…
We consider a nontempered $A$-parameter $\psi$ of $SO(2n+1, F)$ of a certain type and the base point representation $\pi$ in the $A$-packet of $\psi$. Let $\hat{\pi}$ be the Aubert involution of $\pi$. We compute explicitly the Langlands…
We review several inequalities concerning Gaussian measures - isoperimetric inequality, Ehrhard's inequality, Bobkov's inequality, S-inequality and correlation conjecture.
A permutation is defined to be cycle-up-down if it is a product of cycles that, when written starting with their smallest element, have an up-down pattern. We prove bijectively and analytically that these permutations are enumerated by the…
Permutations of correlated sequences of random variables appear naturally in a variety of applications such as graph matching and asynchronous communications. In this paper, the asymptotic statistical behavior of such permuted sequences is…