Exact Results for the Symmetric Dyson Exclusion Process

What the math gives to ML

The paper provides an exactly solvable exclusion dynamics in which local particle moves are controlled by a global logarithmic-repulsion factor, together with a free-fermion and determinantal representation of the evolution. Its transferable asset is a collision-free, diversity-promoting routing process with analytically specified multi-particle transition rates rather than independent softmax decisions. A practical neural-network use is a structured mixture-of-experts router in which expert assignments evolve by short-range moves under Dyson-style repulsion, preserving hard capacity constraints while discouraging routing collapse.