Maybe the proof is wrong, but it looks quite likely to this will constitute an advance in our MCMC toolkit. In particular, I'd be curious if we can use his new

Maybe the proof is wrong, but it looks quite likely to this will constitute an advance in our MCMC toolkit. In particular, I'd be curious if we can use his new MCMC method to create a probabilistical version of Schor's factorization algorithm. If NP=RP, this should be an easy consequence, but even if NP!=RP, it's possible (and some say even likely) that a classical version of Schor's algorithm exists.