Related papers: On Stochastic Comparisons of Order Statistics from…

We reconsider the issue of proving large scale spatial homogeneity of the universe, given isotropic observations about us and the possibility of source evolution both in numbers and luminosities. Two theorems make precise the freedom…

Sundararajan and Chakraborty (2007) introduced a new version of Quick sort removing the interchanges. Khreisat (2007) found this algorithm to be competing well with some other versions of Quick sort. However, it uses an auxiliary array…

We give simple criteria to identify the exponential order of magnitude of the absolute value of the determinant for wide classes of random matrix models, not requiring the assumption of invariance. These include Gaussian matrices with…

We derive sufficient conditions for the convex and monotonic g-stochastic ordering of diffusion processes under nonlinear g-expectations and g-evaluations. Our approach relies on comparison results for forward-backward stochastic…

We derive optimal-order homogenization rates for random nonlinear elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely, for a random monotone operator on $\mathbb{R}^d$ with stationary law (i.e. spatially…

Applied researchers often claim that the risk difference is more heterogeneous than the relative risk and the odds ratio. Some also argue that there are theoretical grounds for why this claim is true. In this note, we point out that these…

This paper considers the difficulty in the set-system approach to generalizing graph theory. These difficulties arise categorically as the category of set-system hypergraphs is shown not to be cartesian closed and lacks enough projective…

We consider the extreme value statistics of correlated random variables that arise from a Langevin equation. Recently, it was shown that the extreme values of the Ornstein-Uhlenbeck process follow a different distribution than those…

We study sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order $d-1$ for any $d \in \mathbb{N}$. The bounds are based on $d$-th order derivatives or difference operators. In…

We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which…

A sequence $(x_n)$ in a lattice-normed space $(X,p,E)$ is statistical $p$-convergent to $x\in X$ if there exists a statistical $p$-decreasing sequence $q\stpd 0$ with an index set $K$ such that $\delta(K)=1$ and $p(x_{n_k}-x)\leq q_{n_k}$…

We study n by n symmetric random matrices H, possibly discrete, with iid above-diagonal entries. We show that H is singular with probability at most exp(-n^c), and the spectral norm of the inverse of H is O(sqrt{n}). Furthermore, the…

In stochastic volatility models based on time-homogeneous diffusions, we provide a simple necessary and sufficient condition for the discretely sampled fair strike of a variance swap to converge to the continuously sampled fair strike. It…

Define a random variable $\xi_n$ by choosing a conjugacy class $C$ of the Sylow $p$-subgroup of $S_{p^n}$ by random, and let $\xi_n$ be the logarithm of the order of an element in $C$. We show that $\xi_n$ has bounded variance and mean…

We establish exponential bounds for the hypergeometric distribution which include a finite sampling correction factor, but are otherwise analogous to bounds for the binomial distribution due to Le\'on and Perron (2003) and Talagrand (1994).…

The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…

The distribution of the spacing, or the difference between consecutive order statistics, is known only for uniform and exponential random variates. We add here logistic and Gumbel variates, and present an estimator for distributions with a…

In this paper we are interested in the joint distribution of two order statistics from overlapping samples. We give an explicit formula for the distribution of such a pair of random variables under the assumption that the parent…

We prove the convergence at an exponential rate towards the invariant probability measure for a class of solutions of stochastic differential equations with finite delay. This is done, in this non-Markovian setting, using the cluster…

This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…