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The Objective Method: Probabilistic Combinatorial Optimization and Local Weak Convergence
This survey describes a general approach to a class of problems that arise in combinatorial probability and combinatorially optimization. Expand
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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
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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
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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)
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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
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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
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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)
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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
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Lower Bounds for Algebraic Decision Trees
A topological method is given for obtaining lower bounds for the height of algebraic decision trees, extending the Dobkin-Lipton result for linear trees. Expand
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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
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