A percolation model for the emergence of the Bitcoin Lightning Network

Abstract

The Lightning Network is a so-called second-layer technology built on top of the Bitcoin blockchain to provide "off-chain" fast payment channels between users, which means that not all transactions are settled and stored on the main blockchain. In this paper, we model the emergence of the Lightning Network as a (bond) percolation process and we explore how the distributional properties of the volume and size of transactions per user may impact its feasibility. The agents are all able to reciprocally transfer Bitcoins using the main blockchain and also -if economically convenient -to open a channel on the Lightning Network and transact "off chain". We base our approach on fitness-dependent network models: as in real life, a Lightning channel is opened with a probability that depends on the "fitness" of the concurring nodes, which in turn depends on wealth and volume of transactions. The emergence of a connected component is studied numerically and analytically as a function of the parameters, and the phase transition separating regions in the phase space where the Lightning Network is sustainable or not is elucidated. We characterize the phase diagram determining the minimal volume of transactions that would make the Lightning Network sustainable for a given level of fees or, alternatively, the maximal cost the Lightning ecosystem may impose for a given average volume of transactions. The model includes parameters that could be in principle estimated from publicly available data once the evolution of the Lighting Network will have reached a stationary operable state, and is fairly robust against different choices of the distributions of parameters and fitness kernels.Bitcoin, the pioneering cryptocurrency, has brought about an unprecedented revolution in the payment industry 1 . Despite its traction and success over the last ten years, the original blockchain -the technological infrastructure underlying Bitcoin -suffers from some limitations that may hinder the future growth and adoption of the cryptocurrency. One of the major issues is the scalability of the system: the current number of transactions validated via this platform is between 3 and 7 transactions per second, compared for instance to thousands of transactions handled by the Visa circuit 2 . The lack of scalability is mainly caused by constraints on throughput of transactions, with the block size fixed at 1MB, and by the high latency -with a new block created on average only every ten minutes. Those limitations are imposed to safeguard the security of the platform against malicious attacks and are difficult to relax without major changes in the protocol.The main solutions proposed to address the scalability issue include (i) changes to the main protocol (consensus algorithm, parameters) and (ii) sidechains and second-layer solutions (see 3 for a recent technical review). Notable examples of type-(i) solutions include new consensus protocols, which would allow a faster issuance of new blocks among other new features 4 . Sidechains are blockchains "conne...

Percolation thresholds on triangular lattice for neighbourhoods containing sites up-to the fifth coordination zone

“…Finally, the p c (ξ) dependence follows roughly a power law (11). The deviation from this dependence is observed only for p c estimated for tr-2,5 lattice.…”

“…The concepts of site and bond percolation [1,2] introduced in middle fifties [3,4] and since then have been applied in various fields of science ranging from agriculture [5] via studies of polymer composites [6], materials science [7], forest fires [8], oil and gas exploration [9], quantifying urban areas [10], Bitcoins transfer [11], diseases propagation [12] to transportation networks [13] (see Refs. 14 and 15 for reviews).…”

Probabilistic Logic Models for the Lightning Network

“…In [18], the authors represent the LN with a percolation process [19] and discuss the possible parameters that may influence its structure. They mainly focus on the structure of the network to describe whether a new edge will be added between two nodes, and consider deterministic connections (i.e., two nodes are connected if there is a path).…”

Evolutionary Random Graph for Bitcoin Overlay and Blockchain Mining Networks

“…As discussed previously, scientists failed in mapping the BitOverNet [5][6][7][8][9][10][11][12][13][14] and this hinders progress in protecting it. It is worthy of noting that mapping the BitOverNet, figure 2, is radically different than the bitcoin transaction network [27][28][29][30] , figure 1, and bitcoin lightning 31 .…”