Random Walks on Strict Partitions

Understand

We consider a certain sequence of random walks.

• The state space of the n-th random walk is the set of all strict partitions of n (that is, partitions without equal parts).
• We prove that, as n goes to infinity, these random walks converge to a continuous-time Markov process.
• The state space of this process is the infinite-dimensional simplex consisting of all nonincreasing infinite sequences of nonnegative numbers with sum less than or equal to one.