Consider the complete graph Kn on n vertices and the n-cube graph Qn on 2n vertices. Suppose independent uniform random edge weights are assigned to each edges in Kn and Qn and let and denote the unique minimal spanning trees on Kn and Qn, respectively. In this paper we obtain the Gaussian tail...

Orban and Wolfe (1982) and Kim (1999) provided the limiting distribution for linear placement statistics under null hypotheses only when one of the sample sizes goes to infinity. In this paper we prove the asymptotic normality and the weak convergence of the linear placement statistics of Orban...

Let {Xi: i[greater-or-equal, slanted]1} be i.i.d. points in , d[greater-or-equal, slanted]2, and let LMM({X1,...,Xn},p), LMST({X1,...,Xn},p), LTSP({X1,...,Xn},p), be the length of the minimal matching, the minimal spanning tree, the traveling salesman problem, respectively, on {X1,...,Xn} with...

Using the Poisson point process we model how the SiPM works and derive the non-linear response formula of the SiPM. Using this non-linear response formula we are able to capture the mean and variance saturation phenomena near the infinity and the linear behavior of the mean and variance near 0.

In this paper, we establish a martingale inequality and develop the symmetry argument to use this martingale inequality. We apply this to the length of the longest increasing subsequences and the independence number of sparse random graphs.

Online matching platforms require new approaches to market design, because firms can now control many aspects of the search and interaction process through various IT-enabled features. Although choice capacity—the number of candidates a user can view and select—is a key design feature of...