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Despite a true antipathy to the subject Hardy contributed deeply to modern probability. His work with Ramanujan begat probabilistic number theory. His work on Tauberian theorems and divergent series h...
Random Matrices, Magic Squares and Matching Polynomials。
What is...a Random Matrix?     Random Matrix       2015/7/8
What is...a Random Matrix。
Solitaire: Man Versus Machine     Solitaire  Man  Machine       2015/7/8
Solitaire: Man Versus Machine。
SEPARATION CUT-OFFS FOR BIRTH AND DEATH CHAINS。
This paper gives sharp rates of convergence to stationarity for a Markov chain generating Bose-Einstein configurations of n balls in k boxes. The analysis leads to curious identities for the arc...
We consider the problem of assigning transition probabilities to the edges of a path, so the resulting Markov chain or random walk mixes as rapidly as possible. In this note we prove that fastest mixi...
We consider a Markov process on a connected graph, with edges labeled with transition rates between the adjacent vertices. The distribution of the Markov process converges to the uniform distribution ...
Importance sampling, particularly sequential and adaptive importance sampling, have emerged as competitive simulation techniques to Markov–chain Monte–Carlo techniques. We compare importance sampling ...
We analyze the natural process of flipping a coin which is caught in the hand. We show that vigorously flipped coins tend to come up the same way they started. The limiting chance of comin...
GRAPH LIMITS AND EXCHANGEABLE RANDOM GRAPHS。
We give families of examples where sharp rates of convergence to stationarity of the widely used Gibbs sampler are available. The examples involve standard exponential families and their conjugate pri...
A SEQUENTIAL IMPORTANCE SAMPLING ALGORITHM FOR GENERATING RANDOM GRAPHS WITH PRESCRIBED DEGREES。
The purpose of this paper is to present a probabilistic proof of the well-known result stating that the time needed by a continuous-time finite birth and death process for going from the left en...

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