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Determinantal probability densities at two-qubit separability-entanglement boundary and associated Fisher information
Determinantal probability densities two-qubit separability-entanglement boundary associated Fisher information
2013/4/28
The determinants (|rho^{PT}|) of the partial transposes of 4 x 4 density matrices (rho) have possible values in the interval [-1/16, 1/256], and are nonnegative if and only if rho is separable. In arX...
Exponential functionals of Brownian motion, I: Probability laws at fixed time
Brownian motion Bessel process Lamperti's relation Hartman-Watson distributions
2009/5/18
This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several rel...
Orthogonality and probability: beyond nearest neighbor transitions
reversible Markov chains orthogonal polynomials Karlin-McGregor representation
2009/4/29
In this article, we will explore why Karlin-McGregor method of using orthogonal polynomials in the study of Markov processes was so successful for one dimensional nearest neighbor processes, but faile...
Entropy Estimate for k-Monotone Functions via Small Ball Probability of Integrated Brownian Motions
Metric entropy class of distribution functions
2009/3/19
Metric entropy of the class of probability distribution functions on [0,1] with a k-monotone density is studied through its connection with the small ball probability of k-times integrated Brownian mo...