# Archive ouverte HAL – Two faces of Douglas-Kazakov transition: from Yang-Mills theory to random walks and beyond

### Alexander GorskyAlexey MilekhinSergei Nechaev 1

#### Alexander Gorsky, Alexey Milekhin, Sergei Nechaev. Two faces of Douglas-Kazakov transition: from Yang-Mills theory to random walks and beyond. Nuclear Physics B, Elsevier, 2019. ⟨hal-02365447⟩

Being inspired by the connection between 2D Yang-Mills (YM) theory and (1+1)D "vicious walks" (VW), we consider different incarnations of large-$N$ Douglas-Kazakov (DK) phase transition in gauge field theories and stochastic processes focusing at possible physical interpretations. We generalize the connection between YM and VW, study the influence of initial and final distributions of walkers on the DK phase transition, and describe the effect of the $\theta$-term in corresponding stochastic processes. We consider the Jack stochastic process involving Calogero-type interaction between walkers and investigate the dependence of DK transition point on a coupling constant. Relying on the relation between large-$N$ 2D $q$-YM and extremal black hole (BH) with large-$N$ magnetic charge, we speculate about a physical interpretation of a DK phase transitions in a 4D extremal charged BH.

• 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques