3 papers
math.PR2018
The CLT in high dimensions: quantitative bounds via martingale embedding
Ronen Eldan, Dan Mikulincer, Alex Zhai
We introduce a new method for obtaining quantitative convergence rates for the central limit theorem (CLT) in a high dimensional setting. Using our method, we obtain several new bo…
math.PR2018
Cutoff for product replacement on finite groups
Yuval Peres, Ryokichi Tanaka, Alex Zhai
We analyze a Markov chain, known as the product replacement chain, on the set of generating -tuples of a fixed finite group . We show that as , the tota…
cs.DS2017
Average-case reconstruction for the deletion channel: subpolynomially many traces suffice
Yuval Peres, Alex Zhai
The deletion channel takes as input a bit string , and deletes each bit independently with probability , yielding a shorter string. The trace reconstru…