A composition of a positive integer n is a sequence of positive integers that sum to n. In this talk, I will introduce a family of interval-partition-valued diffusions that arise as limits of random walks on integer compositions. These infinite-dimensional diffusions have Poisson--Dirichlet (pseudo-)stationary distributions. Our model is closely related to Pitman--Dubins Chinese restaurant processes and random walks on integer partitions studied by Borodin--Olshanski and Petrov. I will also talk about some applications of our model in population genetics and continuum-tree-valued dynamics. 

This talk is based on joint work with Noah Forman, Douglas Rizzolo, and Matthias Winkel. 

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