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35 papers · 1 filter
Slow Emergence of Cooperation for Win-Stay Lose-Shift on Trees
Elchanan Mossel, Sebastien Roch
We consider a group of agents on a graph who repeatedly play the prisoner's dilemma game against their neighbors. The players adapt their actions to the past behavior of their oppo…
Valleys and the maximum local time for random walk in random environment
Amir Dembo, Nina Gantert, Yuval Peres +1
Let be the local time at for a recurrent one-dimensional random walk in random environment after steps, and consider the maximum . It is k…
Self-similar and Markov composition structures
Alexander Gnedin, Jim Pitman
The bijection between composition structures and random closed subsets of the unit interval implies that the composition structures associated with for a self-simila…
A stable marriage of Poisson and Lebesgue
Christopher Hoffman, Alexander E. Holroyd, Yuval Peres
Let be a discrete set in . Call the elements of centers. The well-known Voronoi tessellation partitions into polyhedral regions (of varying…
Asymptotic genealogy of a critical branching process
Lea Popovic
Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process.…
Noise stability of functions with low influences: invariance and optimality
Elchanan Mossel, Ryan O'Donnell, Krzysztof Oleszkiewicz
In this paper we study functions with low influences on product probability spaces. The analysis of boolean functions with low influences has become a central problem in discrete F…