An avalanche of empirical studies has addressed the validity of the rank-size rule (or Zipf's law) in a multi-city context in many countries. City size in most countries seems to obey Zipf's law, but the question under which conditions (e.g. sample size, spatial scale) this 'law' holds remained...

In this study, an investigation is conducted into the phenomenon of price clustering in Bitcoin (BTC) denominated in the Japanese yen (JPY). It answers two questions using tick-by-tick data. The first is whether price clustering exists in BTC/JPY transactions, and the other is how the scale of...