Non-Euclidean-normed Statistical Mechanics

Non equilibrium statistical mechanics

In part I of these lecture notes, I introduce the basic tools of non equilibrium statistical mechanics: linear response, Brownian motion, Langevin equation, (Pauli) master equation. Part II is devoted to a derivation of quantum master equations from the Schrödinger equation, and to some of their applications to quantum optics and to Brownian motion. Finally, in part III, I examine more recent d...

The Statistical Mechanics of the Three-Dimensional Euclidean Black Hole

In its formulation as a Chern-Simons theory, threedimensional general relativity induces a Wess-Zumino-Witten action on spatial boundaries. Treating the horizon of the three-dimensional Euclidean black hole as a boundary, I count the states of the resulting WZW model, and show that they yield the correct Bekenstein-Hawking entropy. The relevant states can be understood as “would-be gauge” degre...

A Statistical Mechanics Approach to Random Euclidean MAX TSP

Statistical shape analysis using non-Euclidean metrics

The contribution of this paper is the adaptation of data driven methods for non-Euclidean metric decomposition of tangent space shape coordinates. The basic idea is to extend principal component analysis (PCA) to take into account the noise variance at different landmarks and at different shapes. We show examples where these non-Euclidean metric methods allow for easier interpretation by decomp...

Euclidean Structure in Finite Dimensional Normed Spaces