We present analytical results for the distribution of first passage times of random walks (RWs) on random regular graphs (RRGs) [1]. RRGs are random networks, consisting of $N$ nodes, in which all the nodes are of the same degree $c \ge 3$ and the connections are random and uncorrelated. Starting from a random initial node $i$ at time $t=0$, at each time step $t \ge 1$ an RW hops into a...
The diffusion of particles with passage times significantly slower than regular Brownian motion is observed in various systems, such as amorphous materials, living cells and rheology. This behavior is typically attributed to trapping or waiting times that are scale-free and uncorrelated. Our work demonstrates that correlated waiting times, termed quenched disorder, can redefine our...
The celebrated ``standard'' $q$-state (color) Potts model, where the ferromagnetic interaction is between nearest-neighboring spins on the square lattice, is known to change its temperature-driven phase transition, from continuous to discontinuous, at some critical integer $q_c = 4$ [1,2,3]. Renormalization group theory suggests that this result should hold for other lattices or interaction...
