We review a statistical picture of the glassy state derived from the analysis of the off-equilibrium fluctuation-dissipation relations. We define an ultralong-time limit where ‘one-time quantities’ are close to equilibrium while the response and correlation can still display ageing. In this limit it is possible to relate the fluctuation response relation to static breaking of ergodicity. The re...

We analyze limit order markets and floor exchanges, assuming an informed trader and discretionary liquidity traders use market orders and can either submit block orders or work their demands as a series of small orders. By working their demands, large market order traders pool with small traders. We show that every equilibrium on a floor exchange must involve at least partial pooling. Moreover,...

Consider a polynomial Liénard system depending on three parameters a, b, c and with the following properties: (i) The origin is the unique equilibrium for all parameters. (ii). If a crosses zero, then the origin changes its stability, and a limit cycle bifurcates from the equilibrium. We investigate analytically this bifurcation in dependence on the parameters b and c and establish the existenc...

This paper aimed to review and compare the conventional and advanced numerical techniques used for stability analysis of rock slopes. Two important methods of probabilistic limit equilibrium analysis and distinct element method are used to check the stability of northern abutment rock slope of Gotvand dam (iran) and the advantages and disadvantages of each method is discussed. The results of th...

We summarize recent results regarding the equilibrium and non-equilibrium behavior of cold dilute atomic gases in the limit in which the two body scattering length a goes to infinity. In this limit the system is described by a Galilean invariant (non-relativistic) conformal field theory. We discuss the low energy effective lagrangian appropriate to the limit a → ∞, and compute low energy coeffi...

We study an infinite horizon game in which pairs of players connected by a network are randomly matched to bargain over a unit surplus. We prove that for each discount factor all equilibria are payoff equivalent. The equilibrium payoffs and the set of equilibrium agreement links converge as players become increasingly patient. We construct an algorithm that determines the limit equilibrium payo...

In recent works it has been demonstrated that using an appropriate rescaling, linear Boltzmann-type equations give rise to a scalar fractional diffusion equation in the limit of a small mean free path. The equilibrium distributions are typically heavy-tailed distributions, but also classical Gaussian equilibrium distributions allow for this phenomena if combined with a degenerate collision freq...

We describe the application of methods from the study of discrete dynamical systems to the study of histories of evolving spin networks. These have been found to describe the small scale structure of quantum general relativity and extensions of them have been conjectured to give background independent formulations of string theory. We explain why the the usual equilibrium second order critical ...

We show that the centred occupation time process of the origin of a system of critical binary branching random walks in dimension d ≥ 3, started off either from a Poisson field or in equilibrium, when suitably normalised, converges to a Brownian motion in d ≥ 4. In d = 3, the limit process is fractional Brownian motion with Hurst parameter 3/4 when starting in equilibrium, and a related Gaussia...

A quantum-classical limit of the canonical equilibrium time correlation function for a quantum system is derived. The quantum-classical limit for the dynamics is obtained for quantum systems comprising a subsystem of light particles in a bath of heavy quantum particles. In this limit the time evolution of operators is determined by a quantum-classical Liouville operator, but the full equilibriu...