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We present a large deviation principle for the entropy penalized Mather problem when the Lagrangian L is generic (in this case the Mather measure $mu$ is unique and the support of $mu$ is the Aubry set). Consider, for each value of $epsilon $ and h, the entropy penalized Mather problem $min {int_{tntimesrn} L(x,v)dmu(x,v)+epsilon S[mu]},$ where the entropy S is given by $S[mu]=int_{tntimesrn}mu(x,v)lnfrac{mu(x,v)}{int_{rn}mu(x,w)dw}dxdv,$ and the minimization is performed over the space of probability densities $mu(x,v)$ that satisfy the holonomy constraint It follows from D. Gomes and E. Valdinoci that there exists a minimizing measure $mu_{epsilon, h}$ which converges to the Mather measure $mu$. We show a LDP $lim_{epsilon,hto0} epsilon ln mu_{epsilon,h}(A),$ where $Asubset mathbb{T}^Ntimesmathbb{R}^N$. The deviation function I is given by $I(x,v)= L(x,v)+ ablaphi_0(x)(v)-bar{H}_{0},$ where $phi_0$ is the unique viscosity solution for L.
In this paper we present an upper bound for the decay of correlation for the stationary stochastic process associated with the Entropy Penalized Method. Let $L(x, v):Tt^ntimesRr^nto Rr$ be a Lagrangian of the form L(x,v) = {1/2}|v|^2 - U(x) + < P,
We initiate a study of large deviations for block model random graphs in the dense regime. Following Chatterjee-Varadhan(2011), we establish an LDP for dense block models, viewed as random graphons. As an application of our result, we study upper tai
We establish the (level-1) large deviation principles for three kinds of means associated with the backward continued fraction expansion. We show that: for the harmonic and geometric means, the rate functions vanish exactly at one point; for the arit
Let $Lambda$ be a complex manifold and let $(f_lambda)_{lambdain Lambda}$ be a holomorphic family of rational maps of degree $dgeq 2$ of $mathbb{P}^1$. We define a natural notion of entropy of bifurcation, mimicking the classical definition of entrop
We consider a family of positive operator valued measures associated with representations of compact connected Lie groups. For many independent copies of a single state and a tensor power representation we show that the observed probability distribut