arXiv subjects

Arnab Pal

Publications and source records attributed to Arnab Pal.

76 records · Page 5Linked to original sources

arXiv2015

Extreme value statistics of correlated random variables

Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the minimum of a set of random variables. This is an important problem for any time-series and has applications in climate, finance, sports, all the way to physics of disordered systems where one is interested in the statistics of the ground state energy. While the EVS of uncorrelated variables are well understood, little is known for strongly correlated random variables. Only recently this subject has gained much importance both in statistical physics and in probability theory. In this note, we will first review the classical EVS for uncorrelated variables and discuss few examples of correlated variables where analytical progress can be made.

cond-mat.stat-mech↗

arXiv2014

Diffusion in a potential landscape with stochastic resetting

The steady state of a Brownian particle diffusing in an arbitrary potential under the stochastic resetting mechanism has been studied. We show that there are different classes of nonequilibrium steady states depending on the nature of the potential. In the stable potential landscape, the system attains a well defined steady state however existence of the steady state for the unstable landscape is constrained. We have also investigated the transient properties of the propagator towards the steady state under the stochastic resetting mechanism. Finally, we have done numerical simulations to verify our analytical results.

cond-mat.stat-mech↗

arXiv2014

Work fluctuations for a Brownian particle driven by a correlated external random force

We have considered the underdamped motion of a Brownian particle in the presence of a correlated external random force. The force is modeled by an Ornstein-Uhlenbeck process. We investigate the fluctuations of the work done by the external force on the Brownian particle in a given time interval in the steady state. We calculate the large deviation functions as well as the complete asymptotic form of the probability density function of the performed work. We also discuss the symmetry properties of the large deviation functions for this system. Finally we perform numerical simulations and they are in a very good agreement with the analytic results.

cond-mat.stat-mech↗

arXiv2013

Work fluctuations for a Brownian particle in a harmonic trap with fluctuating locations

We consider a Brownian particle in a harmonic trap. The location of the trap is modulated according to an Ornstein-Uhlenbeck process. We investigate the fluctuation of the work done by the modulated trap on the Brownian particle in a given time interval in the steady state. We compute the large deviation as well as the complete asymptotic form of the probability density function of the work done. The theoretical asymptotic forms of the probability density function are in very good agreement with the numerics. We also discuss the validity of the fluctuation theorem for this system.

cond-mat.stat-mech↗