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The Bitcoin Lightning Network (BLN), a so-called "second layer" payment protocol, was launched in 2018 to scale up the number of transactions between Bitcoin owners. In this paper, we analyse the structure of the BLN over a period of 18…

Physics and Society · Physics 2020-09-08 Jian-Hong Lin , Kevin Primicerio , Tiziano Squartini , Christian Decker , Claudio J. Tessone

In this study, the authors examine exhaustive business data on Japanese firms, which cover nearly all companies in the mid- and large-scale ranges in terms of firm size, to reach several key findings on profits/sales distribution and…

Physics and Society · Physics 2015-05-18 Atushi Ishikawa , Shouji Fujimoto , Takayuki Mizuno

We study the probabilistic distribution of the confirmation time of Bitcoin transactions, conditional on the current memory pool (i.e., the queue of transactions awaiting confirmation). The results of this paper are particularly interesting…

Performance · Computer Science 2018-10-22 David Koops

Bitcoin is a representative decentralized currency system. For the security of Bitcoin, fairness in the distribution of mining rewards plays a crucial role in preventing the concentration of computational power in a few miners. Here,…

Cryptography and Security · Computer Science 2025-06-17 Akira Sakurai , Kazuyuki Shudo

In this paper, we explore some stylized facts of the Bitcoin market using the BTC-USD exchange rate time series of historical intraday data from 2013 to 2020. Bitcoin presents some very peculiar idiosyncrasies, like the absence of…

Statistical Finance · Quantitative Finance 2024-09-04 F. N. M. de Sousa Filho , J. N. Silva , M. A. Bertella , E. Brigatti

Digitalisation transforms money from distinguishable physical objects into fungible informational units. A recent theoretical framework predicts that such indistinguishable wealth obeys bosonic occupancy statistics, leading to geometric…

Physics and Society · Physics 2026-05-14 Chanhee Park , Claudio J. Tessone , Yu Zhang , Jeong-Hyuck Park

We model financial transactions as random walks on activity-driven temporal networks. By enforcing fund conservation, our framework analytically derives heavy-tailed distributions for the stationary balances and transaction sizes.…

Physics and Society · Physics 2026-02-25 Carolina E. Mattsson , Claudio Cellerini , Jaume Ojer , Michele Starnini

Bitcoin is the first implementation of what has become known as a 'public permissionless' blockchain. Guaranteeing security and protocol conformity through its elegant combination of cryptographic assurances and game theoretic economic…

Cryptography and Security · Computer Science 2018-02-23 D. McGinn , D McIlwraith , Y. Guo

Wash trading, the practice of simultaneously placing buy and sell orders for the same asset to inflate trading volume, has been prevalent in cryptocurrency markets. This paper investigates whether wash traders in Bitcoin act deliberately to…

Trading and Market Microstructure · Quantitative Finance 2024-11-14 Hunter Ng

Bitcoins and Blockchain technologies are attracting the attention of different scientific communities. In addition, their widespread industrial applications and the continuous introduction of cryptocurrencies are also stimulating the…

Physics and Society · Physics 2018-07-24 Marco Alberto Javarone , Craig Steven Wright

The aim of this work is to establish the personal income distribution from the elementary constituents of a free market; products of a representative good and agents forming the economic network. The economy is treated as a self-organized…

General Finance · Quantitative Finance 2015-06-04 Joachim Kaldasch

Bitcoin uses blockchain technology to maintain transactions order and provides probabilistic guarantee to prevent double-spending, assuming that an attacker's computational power does not exceed %50 of the network power. In this paper, we…

Cryptography and Security · Computer Science 2024-11-19 Ghader Ebrahimpour , Mohammad Sayad Haghighi

We study the computation contests where players compete for searching a solution to a given problem with a winner-take-all reward. The search processes are independent across the players and the search speeds of players are proportional to…

Computer Science and Game Theory · Computer Science 2019-02-26 Yulong Zeng , Song Zuo

Historically, gold and silver have played distinct roles in traditional monetary systems. While gold has primarily been revered as a superior store of value, prompting individuals to hoard it, silver has commonly been used as a medium of…

Computational Engineering, Finance, and Science · Computer Science 2025-08-11 Haoyang Yu , Yutong Sun , Yulin Liu , Luyao Zhang

The synchronization process inherent to the Bitcoin network gives rise to an infinite-server model with the unusual feature that customers interact. Among the closed-form characteristics that we derive for this model is the busy period…

Probability · Mathematics 2017-03-27 Maria Frolkova , Michel Mandjes

While relevant stylized facts are observed for Bitcoin markets, we find a distinct property for the scaling behavior of the cumulative return distribution. For various assets, the tail index $\mu$ of the cumulative return distribution…

Statistical Finance · Quantitative Finance 2021-05-07 Tetsuya Takaishi

The growth potential of a crypto(currency) project can be measured by the use cases spurred by the underlying technology. However, these projects are usually distributed, with a weak feedback schemes. Hence, a metric that is widely used as…

Cryptography and Security · Computer Science 2024-09-04 Maurantonio Caprolu , Roberto Di Pietro , Flavio Lombardi , Elia Onofri

The Bitcoin payment system involves two agent types: Users that transact with the currency and pay fees and miners in charge of authorizing transactions and securing the system in return for these fees. Two of Bitcoin's challenges are (i)…

Cryptography and Security · Computer Science 2022-03-15 Ron Lavi , Or Sattath , Aviv Zohar

Employing profits data of Japanese firms in 2003--2005, we kinematically exhibit the static log-normal distribution in the middle scale region. In the derivation, a Non-Gibrat's law under the detailed balance is adopted together with…

General Finance · Quantitative Finance 2008-12-10 Atushi Ishikawa

The cryptocurrency market presents both significant investment opportunities and higher risks relative to traditional financial assets. This study examines the tail behavior of daily returns for two leading cryptocurrencies, Bitcoin and…

Statistical Finance · Quantitative Finance 2025-07-04 A. H. Nzokem