We considerN single server infinite buffer queues with service rate β. Customers arrive at rateNα, choose L queues uniformly, and join the shortest. We study the processes t ∈ R+ 7→ R t = (R t (k))k∈N for large N , where R t (k) is the fraction of queues of length at least k at time t. Laws of large numbers (LLNs) are known, see Vvedenskaya et al. [15], Mitzenmacher [12] and Graham [5]. We cons...

One of the more convincing interpretations of mixed strategy equilibria describes a mixed equilibrium as a steady state in a large population in which all players use pure strategies but the population as a whole mimics a mixed strategy. To be complete, however, this interpretation requires a good story about how the population arrives at the appropriate distribution over pure strategies. In th...

We consider the relationship between stationary distributions for stochastic models of chemical reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well known Lyapunov function of chemical reaction network theory as a scaling limit of the non-equilibrium potential of the stationary distribution of stochastically modeled complex balanced syst...

The thermohaline circulation (THC) affects the meridional atmospheric temperature gradient and therefore the atmospheric wind and the wind driven ocean circulation. The wind driven circulation (WDC), in turn, affects the THC by the advection of salinity anomalies into deep water formation sites. This paper considers this two way coupling between the WDC and THC, using tools from engineering fee...

This paper proposes a continuous perturbation treatment of the nonlinear equations of a cable, which is characterized by possible aeroelastic instability and internal resonance conditions. The objective is to evaluate the influence of stable modes (called passive) usually ignored when discretizing the model. The first step concerns the description of the structural equilibrium path under the ac...

This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion equation. In this paper, we consider situations in which the equilibrium distribution function is a heavy-tailed distribution with infinite v...

This paper studies how amatching rule affects the evolution of fairness in the ultimatumgame. Gale et al. [1995] show that under the randommatching rule, a partially fair imperfect Nash equilibrium in which all proposers are fair but some responders are selfish is asymptotically stable in the limit as noise in learning vanishes if responders are noisier than proposers. This paper shows that, un...

This paper extends the recent investigation of Tahvonen and Withagen (1996, Journal of Economic Dynamics and Control 20, 1775}1795) for costly and thus sluggish instead of instantaneous reductions in emissions. In addition to the social optimum, the paper investigates the competitive equilibrium. This plausible extension allows to derive limit cycles as the outcome for both, the social optimum ...

Discrete replicator dynamics view evolution as a coordination game played among genes. While previous models of discrete replicator dynamics do not consider environments that respond to the mixed strategy that a population plays, our model incorporates a feedbackbased payoff matrix, which depends on the frequency distribution of alleles. In this model, we construct an environment that is compos...

This paper concerns the equilibrium bulk charge and current density correlation functions in quantum media, conductors and dielectrics, fully coupled to the radiation (the retarded regime). A sequence of static and timedependent sum rules, which fix the values of certain moments of the charge and current density correlation functions, is obtained by using Rytov’s fluctuational electrodynamics. ...