caa a22 4500 605515093 CHVBK 20210128100707.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00205-014-0824-z doi (NATIONALLICENCE)springer-10.1007/s00205-014-0824-z Lefevere Raphaël Laboratoire de Probabilités et Modèles Aléatoires (CNRS UMR 7599), Université Paris Diderot, UFR de Mathématiques, bâtiment Sophie Germain, 5 rue Thomas Mann, 75205, Paris CEDEX, 13, France aut Fick's Law in a Random Lattice Lorentz Gas [Elektronische Daten] [Raphaël Lefevere] We provide a proof that the stationary macroscopic current of particles in a random lattice Lorentz gas satisfies Fick's law when connected to particles reservoirs. We consider a box on a d+1-dimensional lattice and when $${d\geqq7}$$ d ≧ 7 , we show that under a diffusive rescaling of space and time, the probability of finding a current different from its stationary value is exponentially small in time. Its stationary value is given by the conductivity times the difference of chemical potentials of the reservoirs. The proof is based on the fact that in a high dimension, random walks have a small probability of making loops or intersecting each other when starting sufficiently far apart. Springer-Verlag Berlin Heidelberg, 2014 Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/3(2015-06-01), 983-1008 0003-9527 216:3<983 2015 216 205 https://doi.org/10.1007/s00205-014-0824-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0824-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Lefevere Raphaël Laboratoire de Probabilités et Modèles Aléatoires (CNRS UMR 7599), Université Paris Diderot, UFR de Mathématiques, bâtiment Sophie Germain, 5 rue Thomas Mann, 75205, Paris CEDEX, 13, France aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/3(2015-06-01), 983-1008 0003-9527 216:3<983 2015 216 205