5 papers
The Time to Consensus in a Blockchain: Insights into Bitcoin's "6 Blocks Rule''
Partha S. Dey, Aditya S. Gopalan, Vijay G. Subramanian
We investigate the time to consensus in Nakamoto blockchains. Specifically, we consider two competing growth processes, labeled \emph{honest} and \emph{adversarial}, and determine…
Scaling Limit of a Stochastic Clustering Model on
Partha S. Dey, S. Rasoul Etesami, Aditya S. Gopalan
We consider an infinite-dimensional stochastic clustering model on . In discrete time, each point of a unit-intensity simple point process moves halfway toward either o…
The 2R-Conjecture for the Hegselmann--Krause Model: A Proof in Expectation and New Directions
Partha S. Dey, S. Rasoul Etesami, Aditya S. Gopalan
Hegselmann--Krause models are localized, distributed averaging dynamics on spatial data. A key aspect of these dynamics is that they lead to cluster formation, which has important…
Network evolution with mesoscopic delay
Sayan Banerjee, Shankar Bhamidi, Partha Dey +1
Owing to the influence of real-world networks both in science and society, numerous mathematical models have been developed to understand the structure and evolution of these syste…
Network evolution with Macroscopic Delays: asymptotics and condensation
Sayan Banerjee, Shankar Bhamidi, Partha Dey +1
Preferential attachment models typically assume that each arriving vertex observes the current network before choosing its connection. Motivated by distributed systems and social n…