large deviations for finite state markov jump processes with mean field interaction via the comparison principle for an associated hamilton jacobi equation we prove the large deviation principle ldp for the trajectory of a broad class of finite state mean field interacting markov jump processes via a general analytic approach based on viscosity solutions examples include generalized ehrenfest models as well as curie weiss spin flip dynamics with singular jump rates the main step in the proof of the ldp which is of independent interest is the proof of the comparison principle for an associated collection of hamilton jacobi equations additionally we show that the ldp provides a general method to identify a lyapunov function for the associated mckean vlasov equation

singular surfaces mod 2 homology and hyperbolic volume i if m is a simple closed orientable 3 manifold such that 1 m contains a genus g surface group and if h 1 m 2 has rank at least 4g 1 we show that m contains an embedded closed incompressible surface of genus at most g as an application we show that if m is a closed orientable hyperbolic 3 manifold of volume at most 3 08 then the rank of h 1 m 2 is at most 6

large deviations for empirical process of mean field interacting particle system with unbounded jumps a large deviation system is established for the empirical processes of a mean field interacting particle system with unbounded jump rates under assumptions that are satisfied by many interesting models including the first and the second schlogl models the action functional obtained has a form that is very useful for applications

a viscosity solution approach to the asymptotic analysis of queueing systems we consider a system of several interconnected queues with a single class of customers and model the state xt of the system as a jump markov process the problem of interest is to estimate the large deviations behavior of the rescaled system xt ext s corresponding to large time and large excursions of the original unscaled system the techniques employed are those of the theory of viscosity solutions to hamilton jacobi equations from the point of view of large deviation theory the interesting new problem here is the treatment of the process when one or more of the queues are nearly empty since an abrupt change in the jump measure occurs from the point of view of viscosity solutions the discontinuity of the jump measure leads to nonlinear boundary conditions on domains with corners for the associated partial differential equations much of the paper is devoted to proving uniqueness of viscosity solutions for these equations and these sections are of independent interest while our use of test functions in proving the uniqueness is an adaptation of the usual technique the construction of the test functions themselves via the legendre transform is new we obtain a representation for the solution of the equation in terms of a nonstandard optimal control problem which suggests the correct integrand in the large deviation rate functional since it is the treatment of the effects due to the boundaries that is novel we devote the majority of the paper to the detailed development of a simple two dimensional system that exhibits all the essential new features however the arguments may be applied to nueueing systems that are considerably more general and we attempt to indicate this generality as well

growth rates _ homology and volumes of hyperbolic 3 manifolds it is shown that if m is a closed orientable irreducible 3 manifold and n is a nonnegative integer and if h 1 m z p has rank n 2 for some prime p then every n generator subgroup of 1 m has infinite index in 1 m and is in fact contained in infinitely many finite index subgroups of 1 m this result is used to estimate the growth rates of the fundamental group of a 3 manifold in terms of the rank of the z p homology

quadrature free implementation of discontinuous galerkin method for hyperbolic equations a discontinuous galerkin formulation that avoids the use of discrete quadrature formulas is described and applied to linear and nonlinear test problems in one and two space dimensions this approach requires less computational time and storage than conventional implementations but preserves the compactness and robustness inherent in the discontinuous galerkin method test problems include the linear and nonlinear one dimensional scalar advection of smooth initial value problems that are discretized by using unstructured grids with varying degrees of smoothness and regularity and two dimensional linear euler solutions on unstructured grids

low temperature dynamics of the curie weiss model periodic orbits multiple histories and loss of gibbsianness we consider the curie weiss model at initial temperature 0 1 in vanishing external field evolving under a glauber spin flip dynamics with temperature 0 1 we study the limiting conditional probabilities and their continuity properties and discuss their set of points of discontinuity bad points we provide a complete analysis of the transition between gibbsian and non gibbsian behavior as a function of time extending earlier work for the case of independent spin flip dynamics

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

computation of flow noise using source terms in linearized euler s equations an acoustic analogy using linearized euler s equations lee forced with aerodynamic source terms is investigated to computetheacousticfare eld thishybridmethod isappliedto threemodelproblemssimulatedby solving navier stokes equations in this way its validity is estimated by comparing the predicted acoustic e eld with the reference solution given directly by the navier stokes equations the noise radiated by two corotating vortices is studied e rst in a medium at rest and second in a mean sheared e ow with no convection velocity then the sound e eld generated by vortex pairings in a subsonic mixing layer is investigated in this case a simplie ed formulation of lee is proposed to prevent the exponential growth of instability waves the acoustic e elds obtained by solving lee are in good agreement with the reference solution this study shows that the source terms introduced into the lee are appropriate for free sheared e ows and that acoustic mean e ow interactions are properly taken into account in the wave operator nomenclature b half width of the monopolar source c sound velocity e f h vectors in linearized euler s equations lee f frequency f0 fundamental frequency of the mixing layer k complex wave number kr ciki m mach number p pressure re reynolds number rc vortex core radius r0 initial half distance between the two vortices s sound source vector in lee si source terms in the momentum equations t period tij lighthill s tensor t time u unknown vector in lee u1 slow stream velocity of the mixing layer u2 rapid stream velocity of the mixing layer u velocity vector u1 u2 v initial tangential velocity of vortices

on continuous extensions of grafting maps the definition of the grafting operation for quasifuchsian groups is extended by bromberg preprint to all b groups in this paper we show that the extended grafting maps behave as continuous maps for every sequence which converges standardly to a boundary group although the maps are not continuous in general as a consequence of this result we extend goldman s grafting theorem for quasifuchsian groups to all boundary b groups

cusps are dense we show cusps are dense in bers boundary for teichmuller space the proof rests on an estimate for the algebraic effect of a unit quasiconformal deformation supported in the thin part of a hyperbolic riemann surface

approximation by maximal cusps in boundaries of deformation spaces of kleinian groups let m be a compact oriented irreducible atoroidal 3 manifold with nonempty boundary let cc0 m denote the space of convex cocompact kleinian groups uniformizing m we show that any kleinian group in the boundary of cc0 m whose limit set is the whole sphere can be approximated by maximal cusps density of maximal cusps on the boundary of schottky space is derived as a corollary we further show that maximal cusps are dense in the boundary of the quasiconformal deformation space of any geometrically finite hyperbolic 3 manifold with connected conformal boundary

the visual core of a hyperbolic 3 manifold in this note we introduce the notion of the visual core of a hyperbolic 3 manifold n bf h 3 gamma and explore some of its basic properties we investigate circumstances under which the visual core cal v n of a cover n bf h 3 gamma of n embeds in n via the usual covering map pi n rightarrow n we go on to show that if the algebraic limit of a sequence of isomorphic kleinian groups is a generalized web group then the visual core of the algebraic limit manifold embeds in the geometric limit manifold finally we discuss the relationship between the visual core and klein maskit combination along component subgroups

ends of hyperbolic 3 manifolds let n h3 f be a hyperbolic 3 manifold which is homeomorphic to the interior of a compact 3 manifold we prove that n is geometrically tame as a consequence we prove that f s limit set l is either the entire sphere at infinity or has measure zero we also prove that n s geodesic flow is ergodic if and only if lf is the entire sphere at infinity department of mathematics stanford university stanford california 94305 current address department of mathematics university of michigan ann arbor michigan 48109 e mail address dick canary math lsa umich edu this content downloaded from 40 77 167 14 on wed 15 jun 2016 05 36 06 utc all use subject to http about jstor org terms

large deviation properties of weakly interacting processes via weak convergence methods we study large deviation properties of systems of weakly interacting particles modeled by ito stochastic differential equations sdes it is known under certain conditions that the corresponding sequence of empirical measures converges as the number of particles tends to infinity to the weak solution of an associated mckean vlasov equation we derive a large deviation principle via the weak convergence approach the proof which avoids discretization arguments is based on a representation theorem weak convergence and ideas from stochastic optimal control the method works under rather mild assumptions and also for models described by sdes not of diffusion type to illustrate this we treat the case of sdes with delay

geometrical finiteness for hyperbolic groups abstract in this paper we give an account of the notion of geometrical finiteness as applied to discrete groups acting on hyperbolic space of any dimension we prove the equivalence of various definitions of geometrical finiteness and describe the geometry of fundamental domains we give a complete account of when dirichiet domains are finite sided

algebraic limits of kleinian groups which rearrange the pages of a book in this paper we give examples of two new phenomena in kleinian groups we rst exhibit a sequence of homeomorphic marked hyperbolic 3 manifolds whose algebraic limit is not homeomorphic to any element in the sequence we then use this construction to exhibit situations where the space of convex co compact representations of a given 3 manifold group has many components but its closure is connected let m be a compact irreducible oriented 3 manifold and let d 1 m denote the space of all discrete faithful representations of 1 m into psl2 c a sequence of representations n d 1 m converging to d 1 m gives rise to a sequence n n h n 1 m of hyperbolic 3 manifolds each of which is homotopy equivalent to m the sequence n n is said to converge algebraically to n h 1 m see 7 13 14 for more information about algebraic convergence of kleinian groups in many situations see 1 6 15 24 25 27 it has been shown that n n must be homeomorphic to n for all large enough n and we had suspected that this would always be the case in this paper we give a collection of examples where n n is not homeomorphic to n for any n our sequences are quite well behaved the n 1 m are convex co compact and mutually quasiconformally conjugate and the algebraic limit 1 m is geometrically nite in our examples m is obtained by gluing a collection of i bundles to a solid torus along a family of parallel annuli these manifolds are particularly simple examples of books of i bundles see 9 where to explain the terminology one should think of the solid torus as the binding and the i bundles

numerical modeling of sound diffraction at a half plane trailing edge the problem of sound propagation in the presence of a rigid semi infinite plate and a double stream sheared mean flow is solved numerically by means of a linearized lilley s equation this is discretized in the frequency domain by using a green function discretization gfd scheme leading to a very ecient numerical method it is demonstrated that the present approach is able to tackle the edge diraction problem without any additional treatment of the vortex sheet and that it provides results that are in close agreement with the analytical solution for a uniform base flow in addition it is shown that the results obtained by considering a piecewise constant base flow and a mixing layer base flow compare favourably with the solutions obtained by solving the linearized euler equations using a discontinuous galerkin method

green s function discretization scheme for sound propagation in nonuniform flows a new frequency domain discretization technique that permits the numerical solution of the equation governing the propagation of small disturbances within nonuniform potential flows is described the method can be applied successfully to the numerical solution of aeroacoustic problems because a good accuracy is preserved up to 3 4 points per period for three dimensional unstructured meshes the discretization scheme is based on a local interpolation formula that is strictly joined to the physics of wave propagation because it is constructed with the superimposition of elementary sources that are local solutions of the local convective wave equation the method presents aspects in common with both finite difference and finite element methods with the peculiarity that the local interpolation formula can be interpreted as a specific shape function introduced to take advantage of the physics of the problem the method is applied to the potential equation linearized around an arbitrary aerodynamic mean flow and several comparisons with theoretical results as well as several convergence tests are conducted to show that a good accuracy is preserved up to 3 4 points per period also for irregular meshes with both random and systematic distortions numerical calculations are presented for three dimensional problems with both uniform and nonuniform flow and comparisons are made with theoretical and other available numerical results with the appropriate generalizations the method can be regarded as a new efficient general approach for the discretization of generic partial differential equations

cores of hyperbolic 3 manifolds and limits of kleinian groups troels jorgensen conjectured that the algebraic and geometric limits of an algebraically convergent sequence of isomorphic kleinian groups agree if there are no new parabolics in the algebraic limit we prove that this conjecture holds in most cases in particular we show that it holds when the domain of discontinuity of the algebraic limit of such a sequence is non empty we further show with the same assumptions that the limit sets of the groups in the sequence converge to the limit set of the algebraic limit as a corollary we verify the conjecture for finitely generated kleinian groups which are not non trivial free products of surface groups and infinite cyclic groups these results are extensions of similar results for purely loxodromic groups thurston previously established these results in the case when the kleinian groups are freely indecomposable using different techniques from ours ohshika has proven versions of these results for purely loxodromic function groups

the rate function for some measure valued jump processes a principle of large deviations from the mckean vlasov limit is derived for a class of measure valued jump processes it is shown that the associated rate function admits several representations including the one obtained by entropy methods and the one derived by a pathwise approach

large deviation estimates for a conditional probability distribution applications to random interaction gibbs measures let x i y i d be independent identically distributed random variables with arbitrary distribution we show that for almost every y i i the conditional law of the empirical field given y i i satisfies to large deviation inequalities this applies to the study of gibbs measures with random interaction in the case of some mean field models as well as of short range summable interaction we show that the pressure is nonrandom and is given by a variational formula these random gibbs measures have the same large deviation rate which does not depend on the particular realization of the interaction their local behaviour is described in terms of conditional probabilities given the interaction of solutions to the variational formula