Integrable Probability & Random Matrices

Develop exact distributions, stochastic evolution, random spectral objects and their scaling limits.

Begin with the two-particle Bethe ansatz for periodic TASEP. It derives contact scattering and periodic quantization directly from a continuous-time Markov generator, then reconstructs a decay mode on a four-site ring. This is a finite example; it does not establish general spectral completeness or a growth scaling limit.

For a guided probability entrance, use the Markov bridge, stationary-current lesson and laboratory. The broader chapter map below describes future coverage as well as available readings.