Intervenant: José Antonio Lubary (UPC Barcelone, Espagne)
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titre:    Harmonic functions on infinite networks
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Résumé :
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 Are there nonconstant bounded harmonic functions on an infinite 
locally finite network under natural transition conditions as continuity at the
ramification nodes and classical Kirchhoff conditions at all
vertices? We present sufficient criteria for such a network to be
a Liouville space, while we show that a large class of infinite
trees admit infinitely many linearly independent bounded harmonic
functions. Finally, we show that the standard unit cube grid
graphs and some of Kepler's plane tiling graphs are Liouville
spaces.