0 M ay 1 99 9 1 THE LIL FOR CANONICAL U - STATISTICS OF ORDER

The Lil for Canonical U - Statistics of Order

LetX, Xi, i∈N, be independent identically distributed random variables and let h(x,y)= h(y,x) be a measurable function of two variables. It is shown that the bounded law of the iterated logarithm, lim supn(n log log n) −1 ∣∣∑ 1≤i<j≤n h(Xi,Xj) ∣∣<∞ a.s., holds if and only if the following three conditions are satisfied: h is canonical for the law of X (that is, Eh(X,y)=0 for almost all y) and th...

On the Law of the Iterated Logarithm for L-statistics without Variance

Let {X,Xn; n ≥ 1} be a sequence of i.i.d. random variables with distribution function F (x). For each positive integer n, let X1:n ≤ X2:n ≤ · · · ≤ Xn:n be the order statistics of X1, X2, · · · , Xn. Let H(·) be a real Borel-measurable function defined on R such that E|H(X)| < ∞ and let J(·) be a Lipschitz function of order one defined on [0, 1]. Write μ = μ(F, J,H) = E(J(U)H(F←(U))) and Ln(F, ...

ar X iv : h ep - t h / 95 05 05 9 v 1 1 0 M ay 1 99 5 orthochronous The Conformal Spin and Statistics Theorem

1 8 M ay 1 99 9 Some properties of second order theta functions on Prym varieties

Let P ∪P ′ be the two component Prym variety associated to anétale double cover˜C → C of a non-hyperelliptic curve of genus g ≥ 6 and let |2Ξ 0 | and |2Ξ ′ 0 | be the linear systems of second order theta divisors on P and P ′ respectively. The component P ′ contains canonically the Prym curve˜C. We show that the base locus of the subseries of divisors containing˜C ⊂ P ′ is exactly the curve˜C. ...

0 M ay 1 99 9 Statistical properties of braid groups in locally free approximation

Statistical and probabilistic characteristics of locally free group with growing number of generators are defined and their application to statistics of braid groups is given.