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Mixing Times for Random Walks on Geometric Random Graphs
Mixing Times Random Walks Geometric Random Graphs
2015/7/10
A geometric random graph, G^d(n,r), is formed as follows: place n nodes uniformly at random onto the surface of the d-dimensional unit torus and connect nodes which are within a distance r of each oth...
Efficient Rare-event Simulation for the Maximum of Heavy-tailed Random Walks
State-dependent importance sampling rare-event simulation heavy-tails Lyapunov bounds random walks
2015/7/6
Let (Xn: n ≥ 0) be a sequence of i.i.d. r.v.’s with negative mean. Set S0 = 0 and define Sn = X1 +· · ·+Xn. We propose an importance sampling algorithm to estimate the tail of M = max{Sn: n ≥ 0} that ...
Strongly Efficent Algorithms for Light-tailed Random Walks: An Old Folk Song Sung to a Faster New Tune
Strongly Efficent Algorithms Light-tailed Random Walks Folk Song Sung Faster New Tune
2015/7/6
We revisit a classical problem in rare-event simulation, namely, efficient estimation of the probability that the sample mean of n independent identically distributed light tailed (i.e. with finite mo...