Differentiability properties of rank-linear utilities

A Lightface Analysis of the differentiability rank

We examine the computable part of the differentiability hierarchy defined by Kechris and Woodin. In that hierarchy, the rank of a differentiable function is an ordinal less than ω1 which measures how complex it is to verify differentiability for that function. We show that for each recursive ordinal α > 0, the set of Turing indices of C[0, 1] functions that are differentiable with rank at most ...

Differentiability Properties of Isotropic Functions

1. Introduction. Let Sym denote the linear space of all symmetric second-order tensors on an n-dimensional real vector space Vect with scalar product. (If Vect is identified with R n , then Sym may be identified with the set of all symmetric n-by-n matrices.) A function f : Sym → R is said to be isotropic if f (A) = f (QAQ T) for all A ∈ Sym and all Q proper orthogonals. An isotropic function h...

Collective Choice with Linear Utilities

This note considers a property, called “limited shared weak preferences” (LSWP), in the context of a model with linear utility functions defined on a polyhedron of alternatives. As special cases, we capture the distributive politics model with externalities in consumption, and we capture collective choice of lotteries by expected utility-maximizing agents. We give a simple sufficient condition ...

Differentiability Properties of the Pre-Image Pressure

Differentiability properties of the minimal average action

Given a Z n+l-periodic variational principle on R n+l we look for solutions u : R" ---+ R minimizing the variational integral with respect to compactly supported variations. To every vector c~ E R" we consider a subset ~/g~ of solutions which have an average slope c~ when averaging over R n. The minimal average action A(c 0 is defined by the average value of the variational integral given by a ...