Title: Confluence in Probabilistic Rewriting,
Abstract: Driven by the interest of reasoning about probabilistic programming
languages, we set out to study a notion of unicity of normal forms for them. To
provide a tractable proof method for it, we define a property of distribution
confluence which is shown to imply the desired uniqueness (even for infinite
sequences of reduction) and further properties. We then carry over several
criteria from the classical case, such as Newman's lemma, to simplify proving
confluence in concrete languages. Using these criteria, we obtain simple proofs
of confluence for $\lambda_1$, an affine probabilistic $\lambda$-calculus, and
for Q$^*$, a quantum programming language for which a related property has
already been proven in the literature.