Even though strongly correlated systems are abundant, only a few exceptional cases admit analytical solutions. In this paper we present a large class of solvable systems with strong correlations. We consider a set of $N$ independent and identically distributed random variables $\{X_1,X_2,...,X_N\}$ whose common distribution has a parameter $Y$ (or a set of parameters) which itself is random with its own distribution. For a fixed value of this parameter $Y$, the $X_i$ variables are independent and we call them conditionally independent and identically distributed. However, once integrated over the distribution of the parameter $Y$, the $X_i$ variables get strongly correlated yet retain a solvable structure for various observables, such as for the sum and the extremes of $X_i^{\prime }\mathrm{s}$. This provides a simple procedure to generate a class of solvable strongly correlated systems. We illustrate how this procedure works via three physical examples where $N$ particles on a line perform independent (i) Brownian motions, (ii) ballistic motions with random initial velocities, and (iii) Lévy flights, but they get strongly correlated via simultaneous resetting to the origin. Our results are verified in numerical simulations. This procedure can be used to generate an endless variety of solvable strongly correlated systems.

• Received 10 August 2023
• Accepted 27 November 2023

DOI:https://doi.org/10.1103/PhysRevE.109.014101