Random walks of heterogeneous population and ensemble self-reinforcement

The talk will be concerned with time-fractional master equations with random transition probabilities describing a heterogeneous population of random walkers. This formulation leads to an effective underlying random walk that demonstrates ensemble self-reinforcement. The heterogeneity of the population gives rise to an underlying random walk with strong memory for which transition probabilities increase with the number of preceding steps (self-reinforcement). We discuss the implication of ensemble self-reinforcement on the first passage time statistics and anomalous exponents.