A characteristic element of the method is that it often calls for one to introduce a new, infinite, probabilistic object whose local properties inform us about the limiting properties of a sequence of finite problems.Expand

Preface 1. First View of Problems and Methods. A first example. Long common subsequences Subadditivity and expected values Azuma's inequality and a first application A second example. The… Expand

Random Walk and First Step Analysis * First Martingale Steps * Brownian Motion * Martingale--Next Steps * Richness of Paths * Ito Integration * Localization and Ito's Integral * Ito's Formula *… Expand

1. Starting with Cauchy 2. The AM-GM inequality 3. Lagrange's identity and Minkowski's conjecture 4. On geometry and sums of squares 5. Consequences of order 6. Convexity - the third pillar 7.… Expand

A limit theorem is established for a class of random processes (called here subadditive Euclidean functionals) which arise in problems of geometric probability. Particular examples include the length… Expand

On etablit l'analogue d'un resultat d'Efron et Stein (1981) que l'on demontre a l'aide d'une technique d'espace de Hilbert introduite par Vitale (1984)

SummaryAsymptotic results for the Euclidean minimal spanning tree onn random vertices inRd can be obtained from consideration of a limiting infinite forest whose vertices form a Poisson process in… Expand

A topological method is given for obtaining lower bounds for the height of algebraic decision trees and an Ω(n2) bound is obtained for trees with bounded-degree polynomial tests, thus extending the Dobkin-Lipton result for linear trees.Expand

Features related to the perimeter of the convex hull C n of a random walk in R 2 are studied, with particular attention given to its length L n . Bounds on the variance of L n are obtained to show… Expand