Computing Your Ideal Haircut Routine

TL;DR

This paper introduces a stochastic model for hair growth with regular haircuts, using resetting deterministic processes, and provides a mathematical framework to determine an optimal haircut routine.

Contribution

It develops a novel stochastic process model for hair growth with resets, offering a quantitative method to optimize haircut routines.

Findings

Derived explicit formulas for the process's expectation and variance.

Constructed a practical model for recommending haircut schedules.

Demonstrated the model's application to real-world hair growth patterns.

Abstract

We introduce stochastically resetting deterministic processes -- the simplest subclass of general resetting stochastic processes -- finding them to be repackaged renewal processes. In particular, we consider the stochastically resetting deterministic process undergoing linear growth of rate 1 subject to Poissonian resetting and deduce its marginal, expectation, and variance. Then, using these results, we construct a stochastic model for hair growth subject to regular haircuts and use this model to prescribe the reader's ideal haircut routine.