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The Lightning Network is a so-called second-layer technology built on top ofthe Bitcoin blockchain to provide "off-chain" fast payment channels betweenusers, which means that not all transactions are settled and stored on the mainblockchain. In this paper, we model the emergence of the Lightning Network as a(bond) percolation process and we explore how the distributional properties ofthe volume and size of transactions per user may impact its feasibility. Theagents are all able to reciprocally transfer Bitcoins using the main blockchainand also - if economically convenient - to open a channel on the LightningNetwork and transact "off chain". We base our approach on fitness-dependentnetwork models: as in real life, a Lightning channel is opened with aprobability that depends on the "fitness" of the concurring nodes, which inturn depends on wealth and volume of transactions. The emergence of a connectedcomponent is studied numerically and analytically as a function of theparameters, and the phase transition separating regions in the phase spacewhere the Lightning Network is sustainable or not is elucidated. Wecharacterize the phase diagram determining the minimal volume of transactionsthat would make the Lightning Network sustainable for a given level of fees or,alternatively, the maximal cost the Lightning ecosystem may impose for a givenaverage volume of transactions. The model includes parameters that could be inprinciple estimated from publicly available data once the evolution of theLighting Network will have reached a stationary operable state, and is fairlyrobust against different choices of the distributions of parameters and fitnesskernels.

A percolation model for the emergence of the Bitcoin Lightning Network