Using a weak convergence approach, we prove a LPD for the solution of 2D stochastic Navier Stokes equations when the viscosity converges to 0 and the noise intensity is multiplied by the square root of the viscosity. Unlike previous results on LDP for hydrodynamical models, the weak convergence is proven by tightness properties of the distribution of the solution in appropriate functional spaces.

A LDP is proved for the inviscid shell model of turbulence. As the viscosity coefficient ν converges to 0 and the noise intensity is multiplied by √ ν, we prove that some shell models of turbulence with a multiplicative stochastic perturbation driven by a H-valued Brownian motion satisfy a LDP in C([0, T ], V) for the topology of uniform convergence on [0, T ], but where V is endowed with a top...

Here θ is a probability measure on a Polish space , Dr k k = 1 2r is a dyadic partition of (hence the use of 2r summands) satisfying θ Dr k = 1/2r and Lq 1 Lq 2 Lq 2r is an independent, identically distributed sequence of random probability measures on a Polish space such that Lq k q ∈ N satisfies the large deviation principle with a convex rate function. A number of related asymptotic results ...

This paper proves that the stationary distribution over the populations in genetic algorithms focuses on the uniform populations with the highest fitness value as the selective pressure goes to infinity and the mutation probability goes to zero. The obtained sufficient condition is based on Albuquerque-Mazza (2000) who followed Cerf (1998) who initiated the large deviation principle approach (F...

The statement of Theorem 2.4 includes the assertion that the function J defined in Definition 2.3 has compact level sets. The proof, given on pages 318–319, is based on a circular argument and is incorrect. While μ in the last display on page 318 depends on r , the r appearing in the first display on page 319 depends on N , which, in turn, depends on μ. All the other assertions in Theorem 2.4 a...

We present the rate function and a large deviation principle for the entropy penalized Mather problem when the Lagrangian is generic (it is known that in this case the Mather measure μ is unique and the support of μ is the Aubry set). We assume the Lagrangian L(x, v), with x in the torus TN and v ∈ Rn, satisfies certain natural hypothesis, such as superlinearity and convexity in v, as well as s...