Pluripotential theory and convex bodies: large deviation principle

Large deviation principle in logarithmic potential theory

Deviation Measures and Normals of Convex Bodies

With any given convex body we associate three numbers that exhibit, respectively, its deviation from a ball, a centrally symmetric body, and a body of constant width. Several properties of these deviation measures are studied. Then, noting that these special bodies may be defined in terms of their normals, corresponding deviation measures for normals are introduced. Several inequalities are pro...

Valuations on convex sets , non - commutative determinants , and pluripotential theory

A new method of constructing translation invariant continuous valuations on convex subsets of the quaternionic space Hn is presented. In particular new examples of Sp(n)Sp(1)-invariant translation invariant continuous valuations are constructed. This method is based on the theory of plurisubharmonic functions of quaternionic variables developed by the author in two previous papers [5] and [6].

Large Deviation Principle and Inviscid Shell Models

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 ([0, T],V ) for the topology of uniform convergence on [0, T], but where V is endowed with a topolog...

Large Deviation Theory

If we draw a random variable n times from Q, the probability distribution of the sum of the random variables is given by Q. This is the convolution of Q with itself n times. As n → ∞, Q tends to a normal distribution by the central limit theorem. This is shown in Figure 1. The top line is a computed normal distribution with the same mean as Q. However, as shown in Figure 3, when plotted on a lo...