An Elementary Proof of the Inequality $\chi \leq \chi^*$ for Conditional Free Entropy
Through the study of large deviations theory for matrix Brownian motion, Biane-Capitaine-Guionnet proved the inequality $\chi(X) \leq \chi^*(X)$ that relates two analogs of entropy in free probability defined by Voiculescu.
Jekel, David, Pi, Jennifer
core
Elucidating the reversed proton relay mechanism: dual regulatory role of pendant carboxylates relevant to water oxidation. [PDF]
Liu T +7 more
europepmc +1 more source
Association between hearing protection device use and noise-induced hearing loss among manufacturing workers in China: a cross-sectional study. [PDF]
Pan Y +9 more
europepmc +1 more source
A high-selectivity 24-GHz SIW-DGS-CPW bandpass filter with wide stopband rejection for automotive radar and ADAS. [PDF]
Abada AM +3 more
europepmc +1 more source
Innovative myopic screening platform based on smartphones. [PDF]
Su Q +8 more
europepmc +1 more source
Development and validation of a measure of early adverse experiences: childhood adversity scale. [PDF]
Yanik M +4 more
europepmc +1 more source
Ruminative thinking mediates the effects of exposure to adverse life events on psychotic-like experiences. [PDF]
Fazio L +27 more
europepmc +1 more source
A machine learning model for assessing fetal health during pregnancy. [PDF]
Ashik AK +13 more
europepmc +1 more source
Assessment of index-based traffic noise annoyance level at major road intersections in a tourist city: A case study towards environmental sustainability. [PDF]
Nath H +7 more
europepmc +1 more source
The relative contribution of modifiable and non-modifiable factors for determining cognition in mid-life individuals at risk for late-life Alzheimer's disease. [PDF]
Cao B +11 more
europepmc +1 more source

