Donald Lynden-Bell (1935–2018)

Lynden-Bell and Tsallis distributions for the HMF model

Systems with long-range interactions can reach a Quasi Stationary State (QSS) as a result of a violent collisionless relaxation. If the system mixes well (ergodicity), the QSS can be predicted by the statistical theory of Lynden-Bell (1967) based on the Vlasov equation. When the initial distribution takes only two values, the Lynden-Bell distribution is similar to the Fermi-Dirac statistics. Su...

A Lynden-Bell integral estimator for extremes of randomly truncated data

This work deals with the estimation of the extreme value index and extreme quantiles for heavy tailed data, randomly right truncated by another heavy tailed variable. Under mild assumptions and the condition that the truncated variable is less heavy-tailed than the truncating variable, asymptotic normality is proved for both estimators. The proposed estimator of the extreme value index is an ad...

Precise determination of the nonequilibrium tricritical point based on Lynden-Bell theory in the Hamiltonian mean-field model.

Existence of a nonequilibrium tricritical point has been revealed in the Hamiltonian mean-field model by a nonequilibrium statistical mechanics. This statistical mechanics gives a distribution function containing unknown parameters, and the parameters are determined by solving simultaneous equations depending on a given initial state. Due to difficulty in solving these equations, pointwise nume...

Title Precise determination of the nonequilibrium tricritical point based on Lynden-Bell theory in the Hamiltonian mean-field model

And Donald

In 1983, Popper and Miller published in Nature a new argument against inductive probability. There followed, the next year, a discussion of the validity of the argument in the pages of the same journal involving Good, Jeffrey, and Levi as well as Popper and Miller themselves. This has led in turn to still further discussions of the argument. Those who are critical include Redhead (1985) and Dun...