Invariance Principles for the Coupon Collector's Problem: A Martingale Approach

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Coupon Collectors, q-Binomial Coefficients and the Unsatisfiability Threshold

The problem of determining the unsatisfiability threshold for random 3-SAT formulas consists in determining the clause to variable ratio that marks the (experimentally observed) abrupt change from almost surely satisfiable formulas to almost surely unsatisfiable. Up to now, there have been rigorously established increasingly better lower and upper bounds to the actual threshold value. An upper ...

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In this paper, we propose a new notion of Forward–Backward Martingale Problem (FBMP), and study its relationship with the weak solution to the forward–backward stochastic differential equations (FBSDEs). The FBMP extends the idea of the well-known (forward) martingale problem of Stroock and Varadhan, but it is structured specifically to fit the nature of an FBSDE. We first prove a general suffi...

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The Coupon Collector’s Problem

In this note we will consider the following problem: how many coupons we have to purchase (on average) to complete a collection. This problem, which takes everybody back to his childhood when this was really “a problem”, has been considered by the probabilists since the eighteenth century and nowadays it is still possible to derive some new results, probably original or at least never published...

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Benefits of Cooperation in Multiplayer Coupon Collectors' Games

The paper introduces a modified version of the classical Coupon Collector’s Problem entailing exchanges and cooperation between multiple players. Results of the development show that, within a proper Markov framework, the complexity of the Cooperative Multiplayer Coupon Collectors’ Problem can be attacked with an eye to the modeling of social strategies and community behaviors. The cost of coop...

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ژورنال

عنوان ژورنال: The Annals of Statistics

سال: 1979

ISSN: 0090-5364

DOI: 10.1214/aos/1176344620