This paper represents the sequence of interevent times (the lulls between bursts of violence in a conflict) as a multiplicative stochastic process - each interevent time is the previous one scaled by an independent random factor, so its logarithm is a sum of independent terms. Invoking the Sornette-Cont result on convergent multiplicative processes repelled from zero, this explains an apparent contradiction in the empirical literature: fine-grained data (resolution of seconds), where the minimum interevent time is arbitrarily close to zero, are lognormally distributed, whereas coarse-grained warfare data (one-day resolution), where the minimum is bounded away from zero, follow a power law. The claim is tested with maximum-likelihood fits to second-resolution video codings of street fights, where the lognormal outperforms the power law for both interevent times and event durations.
Enduring violent conflicts are interrupted by lulls without violence. Studies of interevent times found power law distributions based on coarse-grained data with a resolution of one day. Fine-grained…