RG transformations are conditional expectations with respect to a scale filtration, so the RG flow is a martingale exploration process, a viewpoint previously developed by Bauerschmidt and Bodineau and by the author and Bauer.
Multiple schramm–loewner evolutions and statistical mechanics martingales.Journal of Statistical Physics, 120(5–6):1125–1163, 2005
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The Renormalization Group as a Stochastic Exploration Process
RG transformations are conditional expectations with respect to a scale filtration, so the RG flow is a martingale exploration process, a viewpoint previously developed by Bauerschmidt and Bodineau and by the author and Bauer.