As part of the Applied Analysis research seminar, Fabian Merz will give a talk on the 

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

Date: 6 July 2026

Time: 4.00 pm c.t.

Venue: Helmholtzstrasse 18, Room E.60

All interested parties are warmly invited.

Abstract: 

We show that the non-local Fisher information – defined as the entropy dissipation of the Boltzmann entropy for non-local 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 transition from the non-local to the local limit, we recover the classical Blachman–Stam inequality as well as the corresponding lifting property of the classical Fisher information.