Florian Angeletti

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C. Rowher, F. Angeletti, H. Touchette

Convergence of large deviation estimators,

C. Rowher, F. Angeletti, H. Touchette, Phys. Rev. E, (2015), 52104,
arxiv:1409.8531, BIB, PDF


We study the convergence of statistical estimators used in the estimation of large deviation functions describing the fluctuations of equilibrium,nonequilibrium,and man-made stochastic systems. We give conditions for the convergence of these estimators with sample size,based on the boundedness or unboundedness of the quantity sampled,and discuss how statistical errors should be defined in different parts of the convergence or self-averaging region. Our results shed light on previous reports of ‘phase transitions’ in the statistics of free energy estimators and establish a general framework for reliably estimating large deviation functions from experimental data.

F. Angeletti, H. Touchette, E. Bertin, P. Abry

Large deviations for correlated random variables described by a matrix product ansatz,

F. Angeletti, H. Touchette, E. Bertin, P. Abry, JSTAT, (2014), 2003,
doi:10.1088/1742-5468/2014/02/P02003, arxiv:1310.6952, BIB, PDF


We study the large deviations of sums of correlated random variables described by a matrix product ansatz,which generalizes the product structure of independent random variables to matrices whose non-commutativity is the source of correlations. We show with specific examples that different large deviation behaviors can be found with this ansatz. In particular,it is possible to construct sums of correlated random variables that violate the Law of Large Numbers,the Central Limit Theorem,as well as sums that have nonconvex rate functions or rate functions with linear parts or plateaux.

F. Angeletti, H. Touchette

Diffusions conditioned on occupation measures,

F. Angeletti, H. Touchette, J. Math. Phys., (2016), 23303,
doi:10.1063/1.4941384, arxiv:1510.04893, BIB, PDF


A Markov process fluctuating away from its typical behavior can be represented in the long-time limit by another Markov process,called the effective or driven process,having the same stationary states as the original process conditioned on the fluctuation observed. We construct here this driven process for diffusions spending an atypical fraction of their evolution in some region of state space,corresponding mathematically to stochastic differential equations conditioned on occupation measures. As an illustration,we consider the Langevin equation conditioned on staying for a fraction of time in different intervals of the real line,including the positive half-line which leads to a generalization of the Brownian meander problem. Other applications related to quasi-stationary distributions,metastable states,noisy chemical reactions,queues,and random walks are discussed.