## An Unusally Clean Proof: Dyson Brownian Motion via Conditioning on Non-intersection

Dyson Brownian motion [Dy62] is best known to characterize the eigenvalues of special random matrices [Ta12]. Most interestingly, it is also equal in distribution to \(n\) independent Brownian motions conditioned to not intersect [Gr99]. In a topics course by Bálint Virág, I came across a proof of this result that is *just too clean* for this type of calculations. After picking up my jaw from the ground months later, I finally decided to write up this surprisingly elegant proof.