More Like this

1. Edge Distribution of Thinned Real Eigenvalues in the Real Ginibre Ensemble

   https://doi.org/10.1007/s00023-022-01182-0  

   Baik, Jinho; Bothner, Thomas (April 2022, Annales Henri Poincaré)

   Abstract This paper is concerned with the explicit computation of the limiting distribution function of the largest real eigenvalue in the real Ginibre ensemble when each real eigenvalue has been removed independently with constant likelihood. We show that the recently discovered integrable structures in [2] generalize from the real Ginibre ensemble to its thinned equivalent. Concretely, we express the aforementioned limiting distribution function as a convex combination of two simple Fredholm determinants and connect the same function to the inverse scattering theory of the Zakharov–Shabat system. As corollaries, we provide a Zakharov–Shabat evaluation of the ensemble’s real eigenvalue generating function and obtain precise control over the limiting distribution function’s tails. The latter part includes the explicit computation of the usually difficult constant factors. 

   more » « less
2. Real topological Hochschild homology via the norm and Real Witt vectors

   https://doi.org/10.1016/j.aim.2025.110568  

   Angelini-Knoll, Gabriel; Gerhardt, Teena; Hill, Michael A (December 2025, Advances in Mathematics)
3. Machine learning the real discriminant locus

   https://doi.org/10.1016/j.jsc.2022.08.001  

   Bernal, Edgar A.; Hauenstein, Jonathan D.; Mehta, Dhagash; Regan, Margaret H.; Tang, Tingting (March 2023, Journal of Symbolic Computation)
4. Leximin Allocations in the Real World

   https://doi.org/10.1145/3274641  

   Kurokawa, David; Procaccia, Ariel D.; Shah, Nisarg (November 2018, ACM Transactions on Economics and Computation)
5. Real-Time LaCAM for Real-Time MAPF

   https://doi.org/10.1609/socs.v18i1.35993  

   Liang, Runzhe; Veerapaneni, Rishi; Harabor, Daniel; Li, Jiaoyang; Likhachev, Maxim (July 2025, Proceedings of the International Symposium on Combinatorial Search)

   The vast majority of Multi-Agent Path Finding (MAPF) methods with completeness guarantees require planning full-horizon paths. However, planning full-horizon paths can take too long and be impractical in real-world applications. Instead, real-time planning and execution, which only allows the planner a finite amount of time before executing and replanning, is more practical for real-world multi-agent systems. Several methods utilize real-time planning schemes but none are provably complete, which leads to livelock or deadlock. Our main contribution is Real-Time LaCAM, the first Real-Time MAPF method with provable completeness guarantees. We do this by leveraging LaCAM in an incremental fashion. Our results show how we can iteratively plan for congested environments with a cutoff time of milliseconds while still maintaining the same success rate as full-horizon LaCAM. We also show how it can be used with a single-step learned MAPF policy. 

   more » « less