Existence and continuity of the flow constant in first passage percolation

International audienceWe consider the model of i.i.d. first passage percolation on Z^d , where we associate with the edges of the graph a family of i.i.d. random variables with common distribution G on [0, +∞] (including +∞). Whereas the time constant is associated to the study of 1-dimensional paths with minimal weight, namely geodesics, the flow constant is associated to the study of (d−1)-dimensional surfaces with minimal weight. In this article, we investigate the existence of the flow constant under the only hypothesis that G({+∞}) < p c (d) (in particular without any moment assumption), the convergence of some natural maximal flows towards this constant, and the continuity of this constant with regard to the distribution G