Understanding (with) Toy Models

Understanding stochastic perturbation theory: toy models and statistical analysis

The numerical stochastic perturbation method based on Parisi–Wu quantisation is applied to a suite of simple models to test its validity at high orders. Large deviations from normal distribution for the basic estimators are systematically found in all cases (“Pepe effect”). As a consequence one should be very careful in estimating statistical errors. We present some results obtained on Weingart...

Toy Models for Retrocausality

A number of writers have been attracted to the idea that some of the peculiarities ofquantum theory might be manifestations of ‘backward’ or ‘retro’ causality, underlying thequantum description. This idea has been explored in the literature in two main ways:firstly in a variety of explicit models of quantum systems, and secondly at a concep-tual level. This note introduces a...

Face to Face with Toy Safety: Understanding an Unexpected Threat

Lecture 2 ENSO toy models

Let us consider first a heuristic derivation of an equation for the sea surface temperature in the East Pacific, which will be followed by a more rigorous derivation in the following sections. Assume that the East Pacific SST affects the atmospheric heating and thus the central Pacific wind speed. The resulting wind stress, in turn, excites equatorial Kelvin and Rossby ocean waves. These waves ...

Toy models for wrapping effects

The anomalous dimensions of local single trace gauge invariant operators in N = 4 supersymmetric Yang-Mills theory can be computed by diagonalizing a long range integrable Hamiltonian by means of a perturbative asymptotic Bethe ansatz. This formalism breaks down when the number of fields of the composite operator is smaller than the range of the Hamiltonian which coincides with the order in per...