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作者：Dahmer, Iulia; Kersting, Goetz
作者单位：Goethe University Frankfurt
摘要：In the Kingman coalescent tree the length of order r is defined as the sum of the lengths of all branches that support r leaves. For r = 1 these branches are external, while for r >= 2 they are internal and carry a subtree with r leaves. In this paper we prove that for any s is an element of N the vector of resealed lengths of orders 1 <= r <= s converges to the multivariate standard normal distribution as the number of leaves of the Kingman coalescent tends to infinity. To this end we use a c...
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作者：Chi, Zhiyi
作者单位：University of Connecticut
摘要：Let F be a distribution function on the line in the domain of attraction of a stable law with exponent alpha is an element of (0,1/2]. We establish the strong renewal theorem for a random walk S-1, S-2, ... with step distribution F, by extending the large deviations approach in Doney [Probab. Theory Related Fileds 107 (1997) 451-465]. This is done by introducing conditions on F that in general rule out local large deviations bounds of the type P{S-n is an element of(x, x + h]} = O(n)(F) over b...
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作者：Luczak, Malwina J.; McDiarmid, Colin
作者单位：University of London; Queen Mary University London; University of Oxford
摘要：We consider an online network routing problem in continuous time, where calls have Poisson arrivals and exponential durations. The first-fit dynamic alternative routing algorithm sequentially selects up to d random twolink routes between the two endpoints of a call, via an intermediate node, and assigns the call to the first route with spare capacity on each link, if there is such a route. The balanced dynamic alternative routing algorithm simultaneously selects d random two-link routes, and t...
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作者：Carmona, Rene; Lacker, Daniel
作者单位：Princeton University; Princeton University
摘要：Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to include rank and nearest-neighbor effects. Moreover, the data may depend discontinuously on the state variable, and more generally its entire history. Existence and uniqueness results are proven, along with a procedure for identifying and constructing distributed...
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作者：Jiang, Yunjiang
作者单位：Stanford University
摘要：We prove sharp rates of convergence to the Ewens equilibrium distribution for a family of Metropolis algorithms based on the random transposition shuffle on the symmetric group, with starting point at the identity. The proofs rely heavily on the theory of symmetric Jack polynomials, developed initially by Jack [Proc. Roy. Soc. Edinburgh Sect. A 69 (1970/1971) 1-18], Macdonald [Symmetric Functions and Hall Polynomials (1995) New York] and Stanley [Adv. Math. 77 (1989) 76-115]. This completes th...
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作者：Lanchier, N.
作者单位：Arizona State University; Arizona State University-Tempe
摘要：This article investigates an evolutionary game based on the framework of interacting particle-systems. Each point of the square lattice is occupied by a player who is characterized by one of two possible strategies and is attributed a payoff based on her strategy, the strategy of her neighbors and a payoff matrix. Following the traditional approach of evolutionary game theory, this payoff is interpreted as a fitness: the dynamics of the system is derived by thinking of positive payoffs as birt...
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作者：Ferrari, Patrik L.; Spohn, Herbert; Weiss, Thomas
作者单位：University of Bonn
摘要：We consider Brownian motions with one-sided collisions, meaning that each particle is reflected at its right neighbour. For a finite number of particles a SchUtz-type formula is derived for the transition probability. We investigate an infinite system with periodic initial configuration, that is, particles are located at the integer lattice at time zero. The joint distribution of the positions of a finite subset of particles is expressed as a Fredholm determinant with a kernel defining a signe...
