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The Objective Method: Probabilistic Combinatorial Optimization and Local Weak Convergence
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
Probability theory and combinatorial optimization
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. TheExpand
Stochastic Calculus and Financial Applications
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
Growth Rates of Euclidean Minimal Spanning Trees With Power Weighted Edges
On considere la convergence presque sure d'une suite de variables aleatoires normalisees vers une constante c(α,d)
The Cauchy-Schwarz Master Class
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
Subadditive Euclidean Functionals and Nonlinear Growth in Geometric Probability
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 lengthExpand
An Efron-Stein inequality for nonsymmetric statistics
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)
Asymptotics for Euclidean minimal spanning trees on random points
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 inExpand
Lower Bounds for Algebraic Decision Trees
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
Convex hulls of random walks
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 showExpand