Strong Shannon–McMillan–Breiman’s theorem for locally compact groups
Canadian mathematical bulletin, Tome 66 (2023) no. 4, pp. 1274-1279
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We prove that for a vast class of random walks on a compactly generated group, the exponential growth of convolutions of a probability density function along almost every sample path is bounded by the growth of the group. As an application, we show that the almost sure and $L^1$ convergences of the Shannon–McMillan–Breiman theorem hold for compactly supported random walks on compactly generated groups with subexponential growth.
Forghani, Behrang; Nguyen, May. Strong Shannon–McMillan–Breiman’s theorem for locally compact groups. Canadian mathematical bulletin, Tome 66 (2023) no. 4, pp. 1274-1279. doi: 10.4153/S0008439523000358
@article{10_4153_S0008439523000358,
author = {Forghani, Behrang and Nguyen, May},
title = {Strong {Shannon{\textendash}McMillan{\textendash}Breiman{\textquoteright}s} theorem for locally compact groups},
journal = {Canadian mathematical bulletin},
pages = {1274--1279},
year = {2023},
volume = {66},
number = {4},
doi = {10.4153/S0008439523000358},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000358/}
}
TY - JOUR AU - Forghani, Behrang AU - Nguyen, May TI - Strong Shannon–McMillan–Breiman’s theorem for locally compact groups JO - Canadian mathematical bulletin PY - 2023 SP - 1274 EP - 1279 VL - 66 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000358/ DO - 10.4153/S0008439523000358 ID - 10_4153_S0008439523000358 ER -
%0 Journal Article %A Forghani, Behrang %A Nguyen, May %T Strong Shannon–McMillan–Breiman’s theorem for locally compact groups %J Canadian mathematical bulletin %D 2023 %P 1274-1279 %V 66 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000358/ %R 10.4153/S0008439523000358 %F 10_4153_S0008439523000358
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