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A proof of the security of the Bitcoin protocol is made rigorous, and simplified in certain parts. A computational model in which an adversary can delay transmission of blocks by time $\Delta$ is considered. The protocol is generalized to…

Cryptography and Security · Computer Science 2026-04-17 Christopher Blake , Chen Feng , Xuechao Wang , Qianyu Yu

We construct the Bitcoin User Network (BUN) directly from raw blockchain data up to late 2025, which allows us to explore its mesoscopic properties and trace its temporal evolution. In particular, we analyze the structure of connected…

Social and Information Networks · Computer Science 2025-12-02 Myriam Nonaka , F. Javier Marín-Rodríguez , Alexander Jiricny , Miguel Romance , Regino Criado , Sergio Iglesias-Pérez , Alberto Partida

The Bitcoin transaction graph is a public data structure organized as transactions between addresses, each associated with a logical entity. In this work, we introduce a complete probabilistic model of the Bitcoin Blockchain. We first…

Cryptography and Security · Computer Science 2018-12-14 Marc Jourdan , Sebastien Blandin , Laura Wynter , Pralhad Deshpande

Biased-coin designs are used in clinical trials to allocate treatments with some randomness while maintaining approximately equal allocation. More recent rules are compared with Efron's [Biometrika 58 (1971) 403-417] biased-coin rule and…

Methodology · Statistics 2014-05-21 Anthony C. Atkinson

We use the database leak of Mt. Gox exchange to analyze the dynamics of the price of bitcoin from June 2011 to November 2013. This gives us a rare opportunity to study an emerging retail-focused, highly speculative and unregulated market…

Statistical Finance · Quantitative Finance 2017-06-27 Olivier Scaillet , Adrien Treccani , Christopher Trevisan

The aim of this paper is to analyse the Bitcoin in order to shed some light on its nature and behaviour. We select 9 cryptocurrencies that account for almost 75\% of total market capitalisation and compare their evolution with that of a…

Statistical Finance · Quantitative Finance 2023-09-08 Esther Cabezas-Rivas , Felipe Sánchez-Coll , Isaac Tormo-Xaixo

Analyzing social media trends can create a win-win situation for both creators and consumers. Creators can receive fair compensation, while consumers gain access to engaging, relevant, and personalized content. This paper proposes a new…

Social and Information Networks · Computer Science 2024-06-27 Abhishek Saxena , Anton Kolonin

This paper introduces new methods to study behaviours among the 52 largest cryptocurrencies between 01-01-2019 and 30-06-2021. First, we explore evolutionary correlation behaviours and apply a recently proposed turning point algorithm to…

Statistical Finance · Quantitative Finance 2022-11-15 Nick James , Max Menzies

We show that assuming that the returns are independent when conditioned on the value of their variance (volatility), which itself varies in time randomly, then the distribution of returns is well described by the statistics of the sum of…

Statistical Finance · Quantitative Finance 2025-04-30 Hernán Larralde , Roberto Mota Navarro

We construct and study the Google matrix of Bitcoin transactions during the time period from the very beginning in 2009 till April 2013. The Bitcoin network has up to a few millions of bitcoin users and we present its main characteristics…

Social and Information Networks · Computer Science 2018-06-29 Leonardo Ermann , Klaus M. Frahm , Dima L. Shepelyansky

We investigate the relationship between underlying blockchain mechanism of cryptocurrencies and its distributional characteristics. In addition to price, we emphasise on using actual block size and block time as the operational features of…

Cryptography and Security · Computer Science 2021-08-25 Min-Bin Lin , Kainat Khowaja , Cathy Yi-Hsuan Chen , Wolfgang Karl Härdle

Bitcoin is the first and undoubtedly most successful cryptocurrecny to date with a market capitalization of more than 100 billion dollars. Today, Bitcoin has more than 100,000 supporting merchants and more than 3 million active users.…

Cryptography and Security · Computer Science 2019-11-19 Emmanouil Karampinakis , Michalis Pachilakis , Panagiotis Papadopoulos , Antonis Krithinakis , Evangelos P. Markatos

The fast-growing cryptocurrency sector presents both challenges and opportunities for businesses and consumers alike. This study investigates the knowledge, expertise, and buying habits of people who shop using cryptocurrencies. Our survey…

Computers and Society · Computer Science 2025-10-16 Massimiliano Silenzi , Umut Can Cabuk , Enis Karaarslan , Omer Aydin

Blockchain systems run consensus rules as code to agree on the state of the distributed ledger and secure the network. Changing these rules can be risky and challenging. In addition, it can often be controversial and take much effort to…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-02-15 Jakob Svennevik Notland , Mariusz Nowostawski , Jingyue Li

This paper conducts an extensive analysis of Bitcoin return series, with a primary focus on three volatility metrics: historical volatility (calculated as the sample standard deviation), forecasted volatility (derived from GARCH-type…

Trading and Market Microstructure · Quantitative Finance 2024-01-05 Cristina Chinazzo , Vahidin Jeleskovic

This paper analyses the high-frequency intraday Bitcoin dataset from 2019 to 2022. During this time frame, the Bitcoin market index exhibited two distinct periods, 2019-20 and 2021-22, characterized by an abrupt change in volatility. The…

Statistical Finance · Quantitative Finance 2025-06-24 Yaoyue Tang , Karina Arias-Calluari , M. N. Najafi , Michael S. Harré , Fernando Alonso-Marroquin

Cryptocurrencies and Bitcoin, in particular, are prone to wild swings resulting in frequent jumps in prices, making them historically popular for traders to speculate. A better understanding of these fluctuations can greatly benefit crypto…

Mathematical Finance · Quantitative Finance 2023-10-17 Edson Pindza , Jules Clement Mba , Sutene Mwambi , Nneka Umeorah

A new model, called "Human Dynamics", has been recently proposed that individuals execute activities based on a perceived priority of tasks, which can be characterized by a power-law distribution of waiting time between consecutive tasks…

Computers and Society · Computer Science 2019-11-05 Jonathan J. H. Zhu , Tai-Quan Peng

This paper is concerned with the stability of shares in a cryptocurrency where the new coins are issued according to the Proof of Stake protocol. We identify large, medium and small investors under various rewarding schemes, and show that…

General Economics · Economics 2022-06-07 Wenpin Tang

The Bitcoin Lightning Network is a Layer 2 payment protocol that addresses Bitcoin's scalability by facilitating quick and cost effective transactions through payment channels. This research explores the feasibility of using machine…

Machine Learning · Computer Science 2025-10-24 Vincent Davis , Emanuele Rossi , Vikash Singh
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