Change the free diffusion equation in the simulator

[joe-from-mtl]

Reviewer 1 comment :

A priori, the correct simulation of diffusion with coefficient D is to use displacements distributed as N(0,sqrt(2D dt)) (see e.g. SI of ref. 10 ). The authors use instead sqrt(D dt) N(0, 1), which appears different based on the linearity of normal distributions (aN(0,s) + b = N(b,|a|s)). Please clarify.

[joe-from-mtl]

numpy.random.randn returns a sample from the standard normal distribution N(0,1). To convert this to any normal distribution N(mu, sigma^2) => sigma * N(0,1) + mu. For mu=0 and var=sigma^2=2D dt, we indeed need to change the multiplicative factor in the free (Brownian) equation from sqrt(D dt) to sqrt(2 D dt).