Document Type : Original Article
Authors
Department of Physics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran
Abstract
In this study, we present a discrete-time non-Markov process, referred to as an Elephant Random Walk, implemented on an infinite one-dimensional lattice, with the inclusion of random memory resetting. Upon each random resetting event, the walker completely loses its memory. Through analytical calculations, we determine the moments of displacement in the presence of random resetting. Our findings demonstrate that the process does not attain a steady state. However, the long-time behavior of the moments reveals that, under specific conditions, the displacement distribution follows a Gaussian distribution. By manipulating the resetting mechanism, the transition from diffusive to superdiffusive behavior, or vice versa, can be induced in the process.
Keywords
Main Subjects
- C D Bello, A K Hartmann, S N Majumdar, F Mori, A Rosso and G Schehr, Phys. Rev. E 108 (2023) 014112.
- J Villarroel, M Montero, J A Vega, Entropy 23, 7 (2021) 825.
- A Pal, R Chatterjee, S Reuveni, and A Kundu, J. Phys. A: Math. Theor. 52 (2019) 264002.
- R K Singh, K Górska and T Sandev, Phys. Rev. E 105 (2022) 064133.
- M R Evans, S N Majumdar, and G Schehr, J. Phys. A Math. Theor. 53 (2020) 193001.
- H Chen and F Huang, Phys. Rev. E 105 (2022) 034109.
- O T Friedman, Y Roichman and S Reuven, Phys. Rev. E 106(5) (2022) 054116.
- C D Bello, A V Chechkin, A K Hartmann, Z Palmowski, and R Metzler, New J. Phys. 25 (2023) 082002.
- S N Majumdar, S Sabhapandit, and G Schehr, Phys. Rev. E 92 (2015) 052126.
- D Boyer and C Solis-Salas, Phys. Rev. Lett. 112 (2014) 240601.
- O Vilka, D Camposd, V M ndezd, E Lourieb, R Nathanb and M Assafa, Phys. Rev. Lett. 128 (2022) 148301.
- A Stanislavsky and A Weron, Phys. Rev. E 104 (2021) 014125.
- P Grigolini, Chaos, Solitons & Fractals 81 (2015) 575.
- I Bronstein, Y Israel, E Kepten, S Mai, Y Shav-Tal, E Barkai and Y Garini, Phys. Rev. Lett. 103 (2009) 018102.
- E Kepten, I Bronshtein, and Y Garini, Phys. Rev. E 87 (2013) 052713.
- J Szymanski and M Weiss, Phys. Rev. Lett. 103 (2009) 038102.
- D Brockmann, L Hufnagel, and T Geisel, Nature 439 (2006) 462.
- R N Mantegna and H E Stanley, “Introduction to Econophysics: Correlations and Complexity in Finance”, Cambridge University Press, Cambridge, (2000).
- J-P Bouchaud and M Potters, “Theory of Financial Risk and Derivative Pricing”, Cambridge University Press, Cambridge, (2000).
- G M Schütz and S Trimper, Phys. Rev. E 70 (2004) 045101(R).
- J C Cressoni, G M Viswanathan, and M A A da Silva, J. Phys. A: Math. Theor. 46 (2013) 505002.
- J C Cressoni, M A A da Silva, and G M Viswanathan, Phys. Rev. Lett. 98 (2007) 070603.
- H-J Kim, Phys. Rev. E 90 (2014) 012103.
- U Harbola, N Kumar, and K Lindenberg, Phys. Rev. E 90 (2014) 022136.
- N Kumar, U Harbola, and K Lindenberg, Phys. Rev. E 82 (2010) 021101.
- M A A da Silva, G Viswanathan, and J Cressoni, Physica A: Statistical Mechanics and its Applications 421 (2015) 522.
- J C Cressoni, G M Viswanathan, A S Ferreira, and M A A da Silva, Phys. Rev. E 86 (2012) 022103.
- M A A da Silva, J C Cressoni, G M Schütz And G M Viswanathan and S Trimper, Phys. Rev. E 88 (2013) 022115.
- F N C Paraan and J P Esguerra, Phys. Rev. E 74 (2006) 032101.
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