Finite Groups of Random Walks in the Quarter Plane and Periodic 4-bar Links

par Vladimir Dragović (University of Texas at Dallas)

mercredi 18 mars 2026, 10:30 → 11:30 Europe/Paris

E2290

We present our solutions to two long standing open problems, one from probability theory formulated by Malyshev
in 1970 and another one from a crossroad of geometry and dynamics, going back to Darboux in
1879. The Malyshev problem is of finding effective, explicit necessary and sufficient conditions in
the closed form to characterize all random walks in the quarter plane with a finite group of the
random walk of order 2n, for all n ≥ 2. We also describe all n-periodic Darboux transformations for 4-bar link problems
for all n ≥ 2, thus completely solving the Darboux problem, that he solved for n = 2.
This is based on a joint work with Milena Radnovic (arXiv: 2512:21976).