The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Tobias Grafke - One of the best experts on this subject based on the ideXlab platform.
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string method for generalized gradient flows computation of rare events in reversible Stochastic Processes
Journal of Statistical Mechanics: Theory and Experiment, 2019Co-Authors: Tobias GrafkeAbstract:Rare transitions in Stochastic Processes often can be rigorously described via an underlying large deviation principle. Recent breakthroughs in the classification of reversible Stochastic Processes as gradient flows have led to a connection of large deviation principles to a generalized gradient structure. Here, we show that, as a consequence, metastable transitions in these reversible Processes can be interpreted as heteroclinic orbits of the generalized gradient flow. As a consequence, this suggests a numerical algorithm to compute the transition trajectories in configuration space efficiently, based on the string method traditionally restricted only to gradient diffusions.
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string method for generalized gradient flows computation of rare events in reversible Stochastic Processes
arXiv: Statistical Mechanics, 2018Co-Authors: Tobias GrafkeAbstract:Rare transitions in Stochastic Processes can often be rigorously described via an underlying large deviation principle. Recent breakthroughs in the classification of reversible Stochastic Processes as gradient flows have led to a connection of large deviation principles to a generalized gradient structure. Here, we show that, as a consequence, metastable transitions in these reversible Processes can be interpreted as heteroclinic orbits of the generalized gradient flow. This in turn suggests a numerical algorithm to compute the transition trajectories in configuration space efficiently, based on the string method traditionally restricted only to gradient diffusions.
Thomas Guerin - One of the best experts on this subject based on the ideXlab platform.
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survival probability of Stochastic Processes beyond persistence exponents
arXiv: Statistical Mechanics, 2019Co-Authors: Nicolas Levernier, Maxim Dolgushev, Olivier Benichou, Raphael Voituriez, Thomas GuerinAbstract:For many Stochastic Processes, the probability $S(t)$ of not-having reached a target in unbounded space up to time $t$ follows a slow algebraic decay at long times, $S(t)\sim S_0/t^\theta$. This is typically the case of symmetric compact (i.e. recurrent) random walks. While the persistence exponent $\theta$ has been studied at length, the prefactor $S_0$, which is quantitatively essential, remains poorly characterized, especially for non-Markovian Processes. Here we derive explicit expressions for $S_0$ for a compact random walk in unbounded space by establishing an analytic relation with the mean first-passage time of the same random walk in a large confining volume. Our analytical results for $S_0$ are in good agreement with numerical simulations, even for strongly correlated Processes such as Fractional Brownian Motion, and thus provide a refined understanding of the statistics of longest first-passage events in unbounded space.
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survival probability of Stochastic Processes beyond persistence exponents
Nature Communications, 2019Co-Authors: Nicolas Levernier, Maxim Dolgushev, Olivier Benichou, Raphael Voituriez, Thomas GuerinAbstract:For many Stochastic Processes, the probability [Formula: see text] of not-having reached a target in unbounded space up to time [Formula: see text] follows a slow algebraic decay at long times, [Formula: see text]. This is typically the case of symmetric compact (i.e. recurrent) random walks. While the persistence exponent [Formula: see text] has been studied at length, the prefactor [Formula: see text], which is quantitatively essential, remains poorly characterized, especially for non-Markovian Processes. Here we derive explicit expressions for [Formula: see text] for a compact random walk in unbounded space by establishing an analytic relation with the mean first-passage time of the same random walk in a large confining volume. Our analytical results for [Formula: see text] are in good agreement with numerical simulations, even for strongly correlated Processes such as Fractional Brownian Motion, and thus provide a refined understanding of the statistics of longest first-passage events in unbounded space.
Nicolas Levernier - One of the best experts on this subject based on the ideXlab platform.
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survival probability of Stochastic Processes beyond persistence exponents
arXiv: Statistical Mechanics, 2019Co-Authors: Nicolas Levernier, Maxim Dolgushev, Olivier Benichou, Raphael Voituriez, Thomas GuerinAbstract:For many Stochastic Processes, the probability $S(t)$ of not-having reached a target in unbounded space up to time $t$ follows a slow algebraic decay at long times, $S(t)\sim S_0/t^\theta$. This is typically the case of symmetric compact (i.e. recurrent) random walks. While the persistence exponent $\theta$ has been studied at length, the prefactor $S_0$, which is quantitatively essential, remains poorly characterized, especially for non-Markovian Processes. Here we derive explicit expressions for $S_0$ for a compact random walk in unbounded space by establishing an analytic relation with the mean first-passage time of the same random walk in a large confining volume. Our analytical results for $S_0$ are in good agreement with numerical simulations, even for strongly correlated Processes such as Fractional Brownian Motion, and thus provide a refined understanding of the statistics of longest first-passage events in unbounded space.
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survival probability of Stochastic Processes beyond persistence exponents
Nature Communications, 2019Co-Authors: Nicolas Levernier, Maxim Dolgushev, Olivier Benichou, Raphael Voituriez, Thomas GuerinAbstract:For many Stochastic Processes, the probability [Formula: see text] of not-having reached a target in unbounded space up to time [Formula: see text] follows a slow algebraic decay at long times, [Formula: see text]. This is typically the case of symmetric compact (i.e. recurrent) random walks. While the persistence exponent [Formula: see text] has been studied at length, the prefactor [Formula: see text], which is quantitatively essential, remains poorly characterized, especially for non-Markovian Processes. Here we derive explicit expressions for [Formula: see text] for a compact random walk in unbounded space by establishing an analytic relation with the mean first-passage time of the same random walk in a large confining volume. Our analytical results for [Formula: see text] are in good agreement with numerical simulations, even for strongly correlated Processes such as Fractional Brownian Motion, and thus provide a refined understanding of the statistics of longest first-passage events in unbounded space.
Koch, Tobias Mirco - One of the best experts on this subject based on the ideXlab platform.
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On the information dimension rate of Stochastic Processes
IEEE, 2017Co-Authors: Geiger Bernhard, Koch, Tobias MircoAbstract:Proceeding of: 2017 IEEE International Symposium on Information Theory, Aachen, Germany, 25-30 June 2017Jalali and Poor ("Universal compressed sensing," arXiv:1406.7807v3, Jan. 2016) have recently proposed a generalization of Rényi's information dimension to stationary Stochastic Processes by defining the information dimension of the Stochastic process as the information dimension of k samples divided by k in the limit as k →∞ to. This paper proposes an alternative definition of information dimension as the entropy rate of the uniformly-quantized Stochastic process divided by minus the logarithm of the quantizer step size 1/m in the limit as m →∞ ; to. It is demonstrated that both definitions are equivalent for Stochastic Processes that are ψ*-mixing, but that they may differ in general. In particular, it is shown that for Gaussian Processes with essentially-bounded power spectral density (PSD), the proposed information dimension equals the Lebesgue measure of the PSD's support. This is in stark contrast to the information dimension proposed by Jalali and Poor, which is 1 if the process's PSD is positive on a set of positive Lebesgue measure, irrespective of its support size.The work of Bernhard C. Geiger has been funded by the Erwin Schrödinger Fellowship J 3765 of the Austrian Science Fund and by the German Ministry of Education and Research in the framework of an Alexander von Humboldt Professorship. The work of Tobias Koch has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 714161), from the 7th European Union Framework Programme under Grant 333680, from the Spanish Ministerio de Economía y Competitividad under Grants TEC2013- 41718-R, RYC-2014-16332 and TEC2016-78434-C3-3-R (AEI/FEDER, EU), and from the Comunidad de Madrid under Grant S2103/ICE-2845
Jun Ohkubo - One of the best experts on this subject based on the ideXlab platform.
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algebraic probability classical Stochastic Processes and counting statistics
Journal of the Physical Society of Japan, 2013Co-Authors: Jun OhkuboAbstract:We study a connection between the algebraic probability and classical Stochastic Processes described by master equations. Introducing a definition of a state which has not been used for quantum cases, the classical Stochastic Processes can be reformulated in terms of the algebraic probability. This reformulation immediately gives the Doi–Peliti formalism, which has been frequently used in nonequilibrium physics. As an application of the reformulation, we give a derivation of basic equations for counting statistics, which plays an important role in nonequilibrium physics.
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posterior probability and fluctuation theorem in Stochastic Processes
Journal of the Physical Society of Japan, 2009Co-Authors: Jun OhkuboAbstract:A generalization of fluctuation theorems in Stochastic Processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via Bayes' theorem. In conventional fluctuation theorems, a forward path and its time reversal play an important role, so that a microscopically reversible condition is essential. In contrast, the microscopically reversible condition is not necessary in the new theorem. It is shown that the new theorem recovers various theorems and relations previously known, such as the Gallavotti–Cohen-type fluctuation theorem, the Jarzynski equality, and the Hatano–Sasa relation, when suitable assumptions are employed.
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posterior probability and fluctuation theorem in Stochastic Processes
arXiv: Statistical Mechanics, 2009Co-Authors: Jun OhkuboAbstract:A generalization of fluctuation theorems in Stochastic Processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via the Bayes theorem. In usual fluctuation theorems, a forward path and its time reversal play an important role, so that a microscopically reversible condition is essential. In contrast, the microscopically reversible condition is not necessary in the new theorem. It is shown that the new theorem adequately recovers various theorems and relations previously known, such as the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the Hatano-Sasa relation, when adequate assumptions are employed.
