Im Rahmen des Forschungsseminars der Angewandten Analysis referiert Fabian Merz zu dem 

Thema "Nonlocal Fisher information: lifting, local limit, and the Blachman-Stam inequality".

Termin: 06.07.2026

Uhrzeit: 16 Uhr c.t.

Raum: Helmholtzstrasse 18, Raum E.60

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Abstract: 

We show that the nonlocal Fisher information-defined as the entropy dissipation of the Boltzmann entropy for nonlocal heat equations-admits a natural lifting in the sense of Guillen and Silvestre. Important examples include the discrete Fisher information arising in Markov chains and the fractional Fisher information $i_s$ associated with the fractional Laplacian $ (-\Delta)^s $ on $\mathbb{R}^d, s\in(0,1)$.

We further establish a Blachman–Stam inequality (BSI) for the fractional Fisher information $i_s$ and prove that, for a large class of functions, $i_s$ converges to the classical Fisher information as $s\to1$. Through this nonlocal-to-local limit, we recover the classical Blachman–Stam inequality as well as the corresponding lifting property of the classical Fisher information.