?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Stochastic+modelling+of+blockchain+consensus&rft.creator=Tessone%2C+Claudio+J&rft.creator=Tasca%2C+Paolo&rft.creator=Ianelli%2C+Flavio&rft.description=Blockchain+and+general+purpose+distributed+ledgers+are+foundational+technologies+which+bring+significant+innovation+in+the+infrastructures+and+other+underpinnings+of+our+socio-economic+systems.+These+P2P+technologies+are+able+to+securely+diffuse+information+within+and+across+networks%2C+without+need+for+trustees+or+central+authorities+to+enforce+consensus.+In+this+contribution%2C+we+propose+a+minimalistic+stochastic+model+to+understand+the+dynamics+of+blockchain-based+consensus.+By+leveraging+on+random-walk+theory%2C+we+model+block+propagation+delay+on+different+network+topologies+and+provide+a+classification+of+blockchain+systems+in+terms+of+two+emergent+properties.+Firstly%2C+we+identify+two+performing+regimes%3A+a+functional+regime+corresponding+to+an+optimal+system+function%3B+and+a+non-functional+regime+characterised+by+a+congested+or+branched+state+of+sub-optimal+blockchains.+Secondly%2C+we+discover+a+phase+transition+during+the+emergence+of+consensus+and+numerically+investigate+the+corresponding+critical+point.+Our+results+provide+important+insights+into+the+consensus+mechanism+and+sub-optimal+states+in+decentralised+systems.&rft.publisher=ArXiv&rft.date=2021-06-11&rft.type=Working+%2F+discussion+paper&rft.language=eng&rft.source=++++ArXiv%3A+Ithaca%2C+NY%2C+USA.+(2021)+++++&rft.format=text&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10180002%2F1%2F2106.06465.pdf&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10180002%2F&rft.rights=open