Morse functions constructed by random walks
Boldizsár Kalmár
Journal of Singularities
volume 28 (2025), 207-216
Received: 26 October 2024. In revised form: 27 November 2025.
Abstract:
We construct random Morse functions on surfaces by random walk and compute related distributions. We study the space of Morse functions through these random variables. We consider subspaces characterized by the surfaces with boundary obtained by cutting the closed domain surface of the Morse function at the levels of regular values. We consider Morse functions having a bounded number of critical points and one single local minimum. We find a small set of Morse functions which are close enough to any other Morse function in the sense that they share the same characterizing surfaces with boundary.
2020 Mathematical Subject Classification:
Primary 57R45; Secondary 60G50
Key words and phrases:
Morse functions, random walks
Author(s) information:
Boldizsár Kalmár
Eötvös Loránd University, Pázmány Péter sétány 1/c., 1117 Budapest, Hungary
and
Budapest University of Technology and Economics, Institute of Mathematics, Egry József street 1., 1111 Budapest, Hungary
email: boldizsar.kalmar@gmail.com