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math.PR2026
The maximum-entropy median-martingale
Rikhav Shah, Vilas Winstein
This short note explores the maximum-entropy walk on the unit interval that is a median-martingale. That is, the median of its next state is equal to its current state. The station…
math.PR2026
Sparse Pseudospectral Shattering
Rikhav Shah, Nikhil Srivastava, Edward Zeng
The eigenvalues and eigenvectors of nonnormal matrices can be unstable under perturbations of their entries. This renders an obstacle to the analysis of numerical algorithms for no…
math.PR2025
The Pseudospectrum of Random Compressions of Matrices
Rikhav Shah
The compression of a matrix onto a subspace is the matrix where the columns of form an orthonormal basis for . This…