Quantitative version of Weyl’s law

A quantitative version of Myerson regularity

In auction and mechanism design, Myerson’s classical regularity condition is often too weak for a quantitative analysis of performance. For instance, ratios between revenue and welfare, or sales probabilities may vanish at the boundary of Myerson regularity. This paper introduces λ-regularity as a quantitative measure of how regular a distribution is. λ-regularity includes Myerson regularity an...

Quantitative version of a Silverstein’s result

We prove a quantitative version of a Silverstein’s Theorem on the 4-th moment condition for convergence in probability of the norm of a random matrix. More precisely, we show that for a random matrix with i.i.d. entries, satisfying certain natural conditions, its norm cannot be small. Let w be a real random variable with Ew = 0 and Ew = 1, and let wij, i, j ≥ 1 be its i.i.d. copies. For integer...

A Central-Limit-Theorem Version of the Periodic Little’s Law

Abstract We establish a central-limit-theorem (CLT) version of the periodic Little’s law (PLL), which complements the sample-path and stationary versions of the PLL which we recently established in order to explain the remarkable accuracy in comparisons of data-generated model simulations to direct estimates from the data for the aggregate occupancy level in a hospital emergency department. Our...

A Quantitative Treatment of Deviations from Raoult's Law.

Quantitative Version of the Oppenheim Conjecture for Inhomogeneous Quadratic Forms

A quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms is proved. We also give an application to eigenvalue spacing on flat 2-tori with Aharonov-Bohm flux.