scholarly journals Tunable Persistent Random Walk in Swimming Droplets

2020 ◽  
Vol 10 (2) ◽  
Author(s):  
Adrien Izzet ◽  
Pepijn G. Moerman ◽  
Preston Gross ◽  
Jan Groenewold ◽  
Andrew D. Hollingsworth ◽  
...  
Keyword(s):  
Random Walk ◽  
Persistent Random Walk

Favorite sites of a persistent random walk

2021 ◽  
Vol 501 (2) ◽  
pp. 125180
Author(s):  
Arka Ghosh ◽  
Steven Noren ◽  
Alexander Roitershtein
Keyword(s):  
Random Walk ◽  
Persistent Random Walk

scholarly journals Zero-one-only process: A correlated random walk with a stochastic ratchet

2014 ◽  
Vol 28 (29) ◽  
pp. 1450201
Author(s):  
Seung Ki Baek ◽  
Hawoong Jeong ◽  
Seung-Woo Son ◽  
Beom Jun Kim
Keyword(s):  
Transport Phenomenon ◽  
Random Walk ◽  
Random Walks ◽  
Stochastic Processes ◽  
Function Method ◽  
Correlated Random Walk ◽  
One Dimensional ◽  
Persistent Random Walk ◽  
The One ◽  
Previous Step

The investigation of random walks is central to a variety of stochastic processes in physics, chemistry and biology. To describe a transport phenomenon, we study a variant of the one-dimensional persistent random walk, which we call a zero-one-only process. It makes a step in the same direction as the previous step with probability p, and stops to change the direction with 1 − p. By using the generating-function method, we calculate its characteristic quantities such as the statistical moments and probability of the first return.

scholarly journals Persistent random walk with exclusion

2013 ◽  
Vol 86 (11) ◽  
Author(s):  
Marta Galanti ◽  
Duccio Fanelli ◽  
Francesco Piazza
Keyword(s):  
Random Walk ◽  
Persistent Random Walk

scholarly journals FROM PERSISTENT RANDOM WALK TO THE TELEGRAPH NOISE

2010 ◽  
Vol 10 (02) ◽  
pp. 161-196 ◽  
Author(s):  
S. HERRMANN ◽  
P. VALLOIS
Keyword(s):  
Random Walk ◽  
Markov Process ◽  
Random Walks ◽  
Poisson Process ◽  
Counting Process ◽  
Telegraph Equation ◽  
Space Time ◽  
Persistent Random Walks ◽  
Persistent Random Walk ◽  
Telegraph Noise

We study a family of memory-based persistent random walks and we prove weak convergences after space-time rescaling. The limit processes are not only Brownian motions with drift. We have obtained a continuous but non-Markov process (Zt) which can be easily expressed in terms of a counting process (Nt). In a particular case the counting process is a Poisson process, and (Zt) permits to represent the solution of the telegraph equation. We study in detail the Markov process ((Zt, Nt); t ≥ 0).

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