5 papers
Eigenvalues of Brownian Motions on
Tatiana Brailovskaya, Nicholas A. Cook, Todd Kemp +1
We prove that the empirical law of eigenvalues of Brownian motion on the Lie Group converges almost surely to a deterministic probability measure, chara…
Eigen-Spike Emergence and Quadratic Equivalents for Conjugate Kernels on Nonlinearly Separable Data
Collin Cranston, Zhichao Wang, Todd Kemp +1
Recent work in random matrix theory (RMT) has developed the notion of deterministic equivalents: typically linear surrogate models that approximate the spectral behavior of large n…
A martingale approach to noncommutative stochastic calculus
David A. Jekel, Todd A. Kemp, Evangelos A. Nikitopoulos
We present a new approach to noncommutative stochastic calculus that is, like the classical theory, based primarily on the martingale property. Using this approach, we introduce a…
Matrix Random Walks and the Lima Bean Law
Bruce K. Driver, Brian C. Hall, Ching Wei Ho +4
A matrix random walk is a stochastic process of the form where are independent ``step'' matrices in . With the right en…
Bias and Division in the Free World
Larry Goldstein, Todd Kemp
Sampling bias is a foundational concept in statistics; associated bias transforms, such as size bias, have come to play important roles in probability theory of late. The first aut…