An Introduction to Infinitely Many Variates.

Modeling infinitely many agents

This paper offers a resolution to an extensively studied question in theoretical economics: which measure spaces are suitable for modeling many economic agents? We propose the condition of “nowhere equivalence” to characterize those measure spaces that can be effectively used to model the space of many agents. In particular, this condition is shown to be more general than various approaches tha...

Opening infinitely many nodes

we develop a theory of holomorphic differentials on a certain class of non-compact Riemann surfaces obtained by opening infinitely many nodes.

Infinitely many star products to play with

While there has been growing interest for noncommutative spaces in recent times, most examples have been based on the simplest noncommutative algebra: [xi, xj ] = iθij . Here we present new classes of (non-formal) deformed products associated to linear Lie algebras of the kind [xi, xj ] = ic k ijxk. For all possible threedimensional cases, we define a new star product and discuss its properties...

An Introduction to Sociolinguistics

Infinitely many-armed bandits

We consider multi-armed bandit problems where the number of arms is larger than the possible number of experiments. We make a stochastic assumption on the mean-reward of a new selected arm which characterizes its probability of being a near-optimal arm. Our assumption is weaker than in previous works. We describe algorithms based on upper-confidence-bounds applied to a restricted set of randoml...