5 papers
On card guessing after an asymmetric single-shelf shuffle
Alexander Clay, Markus Kuba, Raghavendra Tripathi
We provide a definitive analysis of the number of correct guesses in the complete-feedback card guessing game after an asymmetric single-shelf shuffle with parameter .…
Limit theorems for descents and inversions of shelf-shuffles
Alexander Clay
We prove central limit theorems for the number of descents and inversions of permutations produced by shelf-shuffles. These are a model for casino card shuffling machines. We show…
On the statistics of random-to-top shuffles
Alexander Clay
We prove limit theorems for the number of fixed points, descents, and inversions of iterated random-to-top shuffles in two asymptotic regimes. Our proofs are analytic, and they uti…
Long-time asymptotics for Airy wanderer line ensembles
Alexander Clay, Evgeni Dimitrov, Rundong Ding +1
We investigate the long-time behavior of the Airy wanderer line ensembles, an infinite-parameter family of Brownian Gibbsian line ensembles arising as edge-scaling limits of inhomo…
Guessing Strategies for Shuffling Machines
Alexander Clay
We investigate a one-time single shelf shuffle by establishing the position matrix explicitly. In some cases, we prove a no-feedback optimal guessing strategy. A general no-feedbac…