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Random generation of optimal saturated designs
Design of experiments Optimal designs Unobserved species Discovery probability
2013/4/28
Efficient algorithms for searching for optimal saturated designs are widely available. They maximize a given efficiency measure (such as D-optimality) and provide an optimum design. Nevertheless, they...
Topic Discovery through Data Dependent and Random Projections
Topic Discovery through Data Dependent and Random Projections
2013/4/27
We present algorithms for topic modeling based on the geometry of cross-document word-frequency patterns. This perspective gains significance under the so called separability condition. This is a cond...
Analysis of Partially Observed Networks via Exponential-family Random Network Models
Analysis Partially Observed Networks via Exponential-family Random Network Models
2013/4/27
Exponential-family random network (ERN) models specify a joint representation of both the dyads of a network and nodal characteristics. This class of models allow the nodal characteristics to be model...
Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy-Widom distribution
Random Matrix Theory characteristic roots largest eigenvalue Tracy-Widom Distribution Wishart Matrices Gaussian Orthogonal Ensemble
2012/11/23
We derive the exact distribution of the largest eigenvalue for finite dimensions real Wishart matrices and for the Gaussian Orthogonal Ensemble (GOE). We compare the exact distribution with the Tracy-...
Space-time current process for independent random walks in one dimension
Independent random walks hydrodynamic limit fluctuations large deviation
2009/6/12
In a system made up of independent random walks fluctuations of order
1/4 n from the hydrodynamic limit come from particle current across characteristics.
We show that a two-parameter space-time par...
On the Speed of the One-dimensional Excited Random Walk in the Transient Regime
Excited Random Walk Pertubed Random Walk Law of Large Numbers
2009/6/12
We study a class of nearest-neighbor discrete time integer random walks introduced by Zerner (2005), the so called multi-excited random walks. The jump probabilities for such random walker have a drif...
Majorizing multiplicative cascades for directed polymers in random media
Directed polymers random environment strong disorder generalized multiplicative cascades
2009/6/12
In this note we give upper bounds for the free energy of discrete directed polymers in random media. The bounds are given by the so-called generalized multiplicative cascades from the statistical theo...
We construct examples of a random walk with pairwise-independent steps which is almost surely bounded, and for any m and k a random walk with k-wise independent steps which has no stationary distribut...
Distribution of a random functional of a Ferguson-Dirichlet process over the unit sphere
Kuo multivariate c-characteristic function Ferguson-Dirichlet process
2009/3/20
Jiang, Dickey, and Kuo [12] gave the multivariate c-characteristic function and showed that it has properties similar to those of the multivariate Fourier transformation. We first give the multivariat...