scholarly journals Quenched Free Energy and Large Deviations for Random Walks in Random Potentials

2012 ◽  
Vol 66 (2) ◽  
pp. 202-244 ◽  
Author(s):  
Firas Rassoul-Agha ◽  
Timo Seppäläinen ◽  
Atilla Yilmaz
Keyword(s):  
Free Energy ◽  
Large Deviations ◽  
Random Walks ◽  
Random Potentials

scholarly journals Quenched point-to-point free energy for random walks in random potentials

2013 ◽  
Vol 158 (3-4) ◽  
pp. 711-750 ◽  
Author(s):  
Firas Rassoul-Agha ◽  
Timo Seppäläinen
Keyword(s):  
Free Energy ◽  
Random Walks ◽  
Random Potentials ◽  
Point To Point

scholarly journals Run-and-Tumble Motion: The Role of Reversibility

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Bart van Ginkel ◽  
Bart van Gisbergen ◽  
Frank Redig
Keyword(s):  
Free Energy ◽  
Diffusion Coefficient ◽  
Large Deviations ◽  
Energy Function ◽  
Internal State ◽  
Rate Function ◽  
Free Energy Function ◽  
Large Deviations Principle ◽  
Preferred Direction ◽  
State Process

AbstractWe study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the ‘active part’ of the diffusion coefficient is in some sense maximal for reversible state processes. Further, we obtain a large deviations principle for the active particle in terms of the large deviations rate function of the empirical process corresponding to the state process. Again we show that the rate function and free energy function are (pointwise) optimal for reversible state processes. Finally, we show that in the case with two states, the Fourier–Laplace transform of the distribution, the moment generating function and the free energy function can be computed explicitly. Along the way we provide several examples.

scholarly journals Large deviations of convex hulls of self-avoiding random walks

2018 ◽  
Vol 97 (6) ◽  
Author(s):  
Hendrik Schawe ◽  
Alexander K. Hartmann ◽  
Satya N. Majumdar
Keyword(s):  
Large Deviations ◽  
Random Walks ◽  
Convex Hulls

scholarly journals Asymptotics for the First Passage Times of Lévy Processes and Random Walks

2013 ◽  
Vol 50 (1) ◽  
pp. 64-84 ◽  
Author(s):  
Denis Denisov ◽  
Vsevolod Shneer
Keyword(s):  
Large Deviations ◽  
Random Walks ◽  
Levy Processes ◽  
Levy Process ◽  
First Passage Times ◽  
Exact Asymptotics ◽  
First Passage ◽  
Heavy Tailed ◽  
First Time ◽  
Passage Times

We study the exact asymptotics for the distribution of the first time, τx, a Lévy process Xt crosses a fixed negative level -x. We prove that ℙ{τx >t} ~V(x) ℙ{Xt≥0}/t as t→∞ for a certain function V(x). Using known results for the large deviations of random walks, we obtain asymptotics for ℙ{τx>t} explicitly in both light- and heavy-tailed cases.

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