Total variation bound between an unpruned ancestral recombination process and SMC' on pairwise coalescence times
This entry formalizes a total variation bound between the pairwise coalescence-time process of an unpruned ancestral recombination graph and the SMC' approximation, for N ≥ 1 samples, a unit-length genome, and scaled recombination rate R ≥ 0. The observed object is the collection of pairwise coalescence times of all sample pairs at every rational position in [0, 1). The total variation distance is at most an explicit double bound, which is at most min(1, R² times a quadratic coefficient in N − 1). The distance is 0 for one sample and for zero recombination. Supporting statements show that…
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