Cutoff profile for the balanced generalized Bernoulli--Laplace model

Source abstract

We study the balanced generalized Bernoulli--Laplace model introduced by Goenka, Hermon, and Schmid (2025) and establish a Gaussian cutoff profile under spectral conditions satisfied by all reversible chains and the cyclic shift chain. Our method adapts the approach of Olesker-Taylor and Schmid (2026) for the two-urn model, combining concentration around a deterministic trajectory before the cutoff window with an Ornstein--Uhlenbeck approximation near equilibrium. We also give an instance of this model that exhibits cutoff but has no limit profile. Further, we determine the mixing time up to an additive constant for every irreducible instance of the model, identifying a $\log \log n$ correction governed by the largest Jordan block size corresponding to the slowest decaying modes.