BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ishrak AlHajj Hassan (University of Ostrava) DTSTART:20261111T123000Z DTEND:20261111T133000Z DTSTAMP:20261109T050631Z UID:PHK-cohomology-seminar/164 DESCRIPTION:Title: Finite-Step Bounds for Iterated Correlation Matrices\ nby Ishrak AlHajj Hassan (University of Ostrava) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and statistics\ n\n\nAbstract\nIterated Pearson correlation matrices arise from repeatedly applying the row–row correlation operator and appear in relational clus tering\, network analysis\, and related normalization procedures. Although these dynamics are often convergent\, their finite-step behavior remains poorly understood: even along convergent trajectories\, successive update ratios may temporarily exceed one\, producing finite-step expansion phenom ena that are not captured by local asymptotic analyses.\n\nIn this talk\, I present a probabilistic framework for studying finite-step behavior in i terated correlation dynamics. The approach constructs explicit state-depen dent upper bounds for successive contraction ratios conditioned on the cur rent normalized step size. These bounds are obtained through nonparametric conditional quantile estimation and are validated on large ensembles of r andomly initialized trajectories across matrix dimensions ranging from 3 t o 2000.\n\nThe results reveal a remarkable empirical dimension-uniformity in the dynamics and yield practical finite-step guarantees. In particular\ , the analysis identifies a nearly universal contraction threshold: once t he normalized step size falls below approximately 0.03\, the next iteratio n is contractive with probability at least 0.95 across all tested dimensio ns. More broadly\, the work provides the first quantitative finite-step pr obabilistic control of iterated Pearson correlation dynamics and suggests new directions toward an analytical theory of nonlinear correlation-matrix iterations.\n LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/164/ END:VEVENT END:VCALENDAR