Theory and applications of probability and stochastic processes.
A new twisted function-field version of Chowla's conjecture yields the required density-zero bound for irreducible non-$S_n$ polynomials in every degree $n \geq 40$.
Opened-trefoil slots create a binomial determinant coordinate, yielding an $O(n^{-1/2})$ collision bound and a database birthday scale of order $n^{1/4}$.
Unfolding and refolding witness graphs lets the authors characterize critical activation density for every fixed graph H, including witnesses larger than the host graph.
Expected self-intersection time is O(√n log n) on bounded-degree graphs and O(√n) for regular graphs with a uniform spectral gap.
A cone-preservation proof handles one fast and two identical slow servers, closing the first nontrivial case beyond Lin-Kumar’s two-server model.
A BBGKY argument couples entropy and Fisher-information inequalities to extend Lacker’s chaos method to smooth mean-field diffusions.
