##### Cutting Across Disciplines

##### REUVENI GROUP

# Welcome to

Basic Theoretical Research in the Mathematical & Natural Sciences

# THE REUVENI GROUP

#### New Paper: Invariants of Motion with Stochastic Resetting and Space-Time Coupled Returns

#### ā

October 28, 2019

Motion under stochastic resetting serves to model a myriad of processes in physics and beyond, but in most cases studied to date resetting was assumed to take zero time or a time decoupled from the spatial position at the resetting moment. However, in our world, getting from one place to another always takes time; and places that are further away take more time to be reached. We extend the theory to account for this inherent spatio-temporal coupling and discover key invariants of motion with stochastic resetting and space-time coupled returns.

#### New Paper: Gumbel Central Limit Theorem for Max-Min and Min-Max

August 21, 2019

The max-min and min-max of matrices arise prevalently in science and engineering. However, in many real-world situations the computation of the max-min and min-max is challenging as matrices are large and full information about their entries is lacking. We take a statistical-physics approach and establish a Gumbel limit law—akin to the central limit theorem—for the max-min and min-max of large random matrices. See also: Poisson-process limit laws yield Gumbel max-min and min-max.

#### New Paper: Occupancy Correlations in the Asymmetric Simple Inclusion Process

#### ā

October 8, 2019

The asymmetric simple inclusion process (ASIP) is a lattice-gas model for unidirectional transport with irreversible aggregation. To date, the analytical tractability of the model has been rather limited: while the average particle density is easy to compute, very little is known about the joint occupancy distribution. To partially bridge this gap, we study occupancy correlations in the ASIP. An exact formula for the covariance matrix of the occupancy vector at the steady-state is derived and corroborated against numerical simulations.

#### New Paper: Time-Dependent Density of Diffusion with Stochastic Resetting is Invariant to Return Speed

October 7, 2019

The canonical Evans-Majumdar model for diffusion with stochastic resetting assumes that resetting takes zero time: upon resetting the diffusing particle is teleported back to the origin to start its motion anew. We consider a situation where the particle returns to the origin at a finite (rather than infinite) speed. This creates a coupling between the particle's random position at the moment of resetting and its return time. However, whether returns are slow or fast, we always find that the time-dependent distribution of the particle's position is identical to that obtained for instantaneous returns.

#### New Paper: Local Time of Diffusion with Stochastic Resetting

June 28, 2019

The local time of a Brownian particle, e.g., a molecule immersed in fluid, is defined as the total time the particle spends in a small vicinity of its initial position. Since Brownian trajectories are stochastic—the local time is a random variable which fluctuates round and about its mean value. We characterized how the statistics of this random variable is altered due to stochastic resetting.