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math.PR2026
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…
math.PR2026
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…
math.PR2025
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…