KPZ fixed point

In probability theory, the KPZ fixed point is a Markov field and conjectured to be a universal limit of a wide range of stochastic models forming the universality class of a non-linear stochastic partial differential equation called the KPZ equation. Even though the universality class was already introduced in 1986 with the KPZ equation itself, the KPZ fixed point was not concretely specified until 2021 when mathematicians Konstantin Matetski, Jeremy Quastel and Daniel Remenik gave an explicit description of the transition probabilities in terms of Fredholm determinants.[1]

  1. ^ Matetski, Konstantin; Quastel, Jeremy; Remenik, Daniel (2021). "The KPZ fixed point". Acta Mathematica. 227 (1). International Press of Boston: 115–203. arXiv:1701.00018. doi:10.4310/acta.2021.v227.n1.a3.