Stein's Method and Descents after Riffle Shuffles
Jason Fulman, University of Pittsburgh, USA
Abstract
Abstract. Berestycki and Durrett used techniques from random graph
theory to prove that the distance to the identity after iterating the
random transposition shuffle undergoes a transition from Poisson to
normal behavior. This paper establishes an analogous result for
distance after iterates of riffle shuffles or iterates of riffle
shuffles and cuts. The analysis uses different tools: Stein's method
and generating functions. A useful technique which emerges is that of
making a problem more tractable by adding extra symmetry, then using
Stein's method to exploit the symmetry in the modified problem, and
from this deducing information about the original
problem.
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