A central limit theorem for convex sets

A Central Limit Theorem for Convex

Points P1; : : : ; Pn in the unit square de ne a convex n-chain if they are below y = x and, together with P0 = (0; 0) and Pn+1 = (1; 1), they are in convex position. Under uniform probability, we prove an almost sure limit theorem for these chains that uses only probabilistic arguments, and which strengthens similar limit shape statements established by other authors. An interesting feature is...

A Central Limit Theorem for Convex Chains in the Square

Points P1, . . . , Pn in the unit square define a convex n-chain if they are below y = x and, together with P0 = (0, 0) and Pn+1 = (1, 1), they are in convex position. Under uniform probability, we prove an almost sure limit theorem for these chains that uses only probabilistic arguments, and which strengthens similar limit shape statements established by other authors. An interesting feature i...

A Representation Theorem for Bounded Convex Sets

Central Limit Theorem in Multitype Branching Random Walk

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

A Central Limit Theorem for Integer Partitions

Abstract. Recently, Hwang proved a central limit theorem for restricted Λ-partitions, where Λ can be any nondecreasing sequence of integers tending to infinity that satisfies certain technical conditions. In particular, one of these conditions is that the associated Dirichlet series has only a single pole on the abscissa of convergence. In the present paper, we show that this condition can be r...