We study the distribution of the nontrivial zeros of ideal class zeta functions associated to elements in the symmetric space of GLn over a number field. We establish asymptotics for the number of nontrivial zeros up to height T , and asymptotics for the distribution of the nontrivial zeros with respect to the critical line. We combine these results to study the mean value of the real parts of ...

This paper establishes the asymptotic distributions of the likelihood ratio (LR), Anderson-Rubin (AR), and Lagrange multiplier (LM) test statistics under “many weak IV asymptotics.” These asymptotics are relevant when the number of IVs is large and the coefficients on the IVs are relatively small. The asymptotic results hold under the null and under suitable alternatives. Hence, power compariso...

We consider lattice walks in R confined to the region 0 < x1 < x2... < xk with fixed (but arbitrary) starting and end points. The walks are required to be ”reflectable”, that is, we assume that the number of paths can be counted using the reflection principle. The main result is an asymptotic formula for the total number of walks of length n with fixed but arbitrary starting and end point for a...

The convexity arguments developed by Pollard [D. Pollard, Asymptotics for least absolute deviation regression estimators, Econometric Theory 7 (1991) 186–199], Hjort and Pollard [N.L. Hjort, D. Pollard, Asymptotics for minimizers of convex processes, 1993 (unpublished manuscript)], and Geyer [C.J. Geyer, On the asymptotics of convex stochastic optimization, 1996 (unpublished manuscript)] are no...

With localization techniques one can obtain general limit theorems for Toeplitz determinants with Fisher-Hartwig singularities from the asymptotics for any symbol with one singularity of general type. There exists a family of these for which the determinants can be evaluated explicitly and their asymptotics determined. But for the Wiener-Hopf analogue, although there are likely analogous locali...

A classical question for a Toeplitz matrix with given symbol is to compute asymptotics for the determinants of its reductions to finite rank. One can also consider how those asymptotics are affected when shifting an initial set of rows and columns (or, equivalently, asymptotics of their minors). Bump and Diaconis [2] obtained a formula for such shifts involving Laguerre polynomi-als and sums ov...

A Riordan array is an infinite complex matrix (ars) of a certain type (see below for exact definitions). The Riordan array formalism has been much used recently to study combinatorial questions in analysis of algorithms and other areas. Most work has been concerned with “exact” results. In this article we discuss asymptotics of such arrays. We apply general machinery for deriving asymptotics of...

We consider polynomials orthogonal on [0,∞) with respect to Laguerre-type weights w(x) = xe, where α > −1 and where Q denotes a polynomial with positive leading coefficient. The main purpose of this paper is to determine Plancherel-Rotach type asymptotics in the entire complex plane for the orthonormal polynomials with respect to w, as well as asymptotics of the corresponding recurrence coeffic...

We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain a variational principle for the limiting free energy, an associated concentration of measure, the asymptotics for the mean and variance of the limiting probability distribution, and phase transitions in the edge-triangle model. Similar analysis is...

In this paper refined large deviation asymptotics are derived for the classical occupancy problem. The asymptotics are established for a sequential filling experiment and an occupancy experiment. In the first case the random variable of interest is the number of balls required to fill a given fraction of the urns, while in the second a fixed number of balls are thrown and random variable is the...