2026-08-14 –, Room 4
Pfaffian point processes (PfPPs) most famously arise in the eigenvalue distributions of random orthogonal or symplectic matrices, but also appear in the description of other stochastic processes, such as annihilating and coalescing random walks, random involutions, or symmetric corner growth. We introduce novel sampling algorithms for discrete and continuous PfPPs, as well as a method for constructing skew-symmetric kernels based on skew-orthogonal polynomials derived from arbitrary weights.
While many sampling algorithms have been developed for determinantal point processes, much less is known about sampling from PfPPs. We introduce an exact sampling algorithm for discrete PfPPs based on a skew-symmetric variant of the Cholesky decomposition, as well as a variety of methods for sampling from continuous Pfaffian kernels based on Markov chain Monte Carlo.
Pfaffian kernels are typically constructed from skew-orthogonal polynomials (SOPs), so we also introduce a new numerical method for constructing SOPs from arbitrary weight functions based on symplectic Arnoldi iteration.
We present a Julia toolbox for Pfaffian point processes with the methods we developed. All of this wouldn't have been possible without Julia's rich ecosystem for numerical linear algebra, computational statistics and automatic differentiation. As such, we were able to reuse existing functionality from and extend packages such as SkewLinearAlgebra.jl, KrylovKit.jl, DynamicHMC.jl, and Mooncake.jl
We investigate accuracy, as well as performance, of these methods on concrete examples and give an outlook on how these methods could be further improved upon.
Master's student at KIT (Germany)
Interested in computational mathematics, programming language design, automatic differentiation and compilers.
GitHub: https://github.com/simeonschaub