We propose an analytical model of ring samplers towards a deeper understanding of them through systematic studies. Our model helps to describe how anonymous a ring sampler is with respect to a given signer distribution as an information-theoretic measure. We show that this measure is robust – it only varies slightly when the signer distribution varies slightly. We then analyze three natural samplers – uniform, mimicking, and partitioning – under our model with respect to a family of signer distributions modeled after empirical Bitcoin data. We hope that our work paves the way towards researching ring samplers from a theoretical point of vie}, author = {Ronge, Viktoria and Egger, Christoph and Lai, Russell W. F. and Schröder, Dominique and Yin, Hoover H.F.}, doi = {10.2478/popets-2021-0047}, faupublication = {yes}, journal = {Proceedings on Privacy Enhancing Technologies}, keywords = {Ring SignatureAnonymityMonero}, pages = {265--288}, peerreviewed = {Yes}, title = {{Foundations} of {Ring} {Sampling}}, volume = {2021}, year = {2021} }