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The genealogy at a single locus of a constant size $N$ population inequilibrium is given by the well-known Kingman's coalescent. When consideringmultiple loci under recombination, the ancestral recombination graph encodesthe genealogies at all loci in one graph. For a continuous genome $G$, we studythe tree-valued process $(T^N_u)_{u\in G}$ of genealogies along the genome inthe limit $N\to\infty$. Encoding trees as metric measure spaces, we showconvergence to a tree-valued process with cadlag paths. In addition, we studymixing properties of the resulting process for loci which are far apart.

A mixing tree-valued process arising under neutral evolution with recombination