iterated mayer expansion for classical gases at low temperatures we derive iterated mayer expansions for classical gases and establish recursive bounds which control their convergence these bounds are useful for gases with two body forces which are strong and possibly attractive at distances that are short compared to their range our procedure is based on splitting the potential into pieces of decreasing strength and increasing range this may be called a renormalization group treatment of a classical gas we apply our results to yukawa lattice gas models and obtain convergence of series expansions for the pressure for a range of parameters temperature fugacities range of the interaction that was inaccessible before application to 3 dimensionalu 1 lattice gauge theory coulomb gas z ferromagnet will be made elsewhere

a sub riemannian curvature dimension inequality volume doubling property and the poincare inequality let mathbb m be a smooth connected manifold endowed with a smooth measure mu and a smooth locally subelliptic diffusion operator l satisfying l1 0 and which is symmetric with respect to mu we show that if l satisfies with a non negative curvature parameter the generalized curvature inequality introduced by the first and third named authors in http arxiv org abs 1101 3590 then the following properties hold the volume doubling property the poincare inequality the parabolic harnack inequality the key ingredient is the study of dimension dependent reverse log sobolev inequalities for the heat semigroup and corresponding non linear reverse harnack type inequalities our results apply in particular to all sasakian manifolds whose horizontal webster tanaka ricci curvature is nonnegative all carnot groups of step two and to wide subclasses of principal bundles over riemannian manifolds whose ricci curvature is nonnegative

bubble finite elements for the primitive equations of the ocean we introduce in this paper two original mixed methods for the numerical resolution of the stationary primitive equations pe of the ocean the pe govern the behavior of oceanic flows in shallow domains for large time scales we use a reduced formulation lions et al 28 involving horizontal velocities and surface pressures by using bubble functions constructed ad hoc we are able to define two stable mixed methods requiring a low number of degrees of freedom the first one is based on the addition of bubbles of reduced support to inlinemediaobject not available see fulltext velocities elementwise the second one makes use of conic bubbles of extended support along the vertical coordinate the latter constitutes a genuine mini element for the pe e g it requires the least number of extra degrees of freedom to stabilize piecewise linear hydrostatic pressures both methods verify a specific inf sup condition and provide stability and convergence finally we compare several numerical features of the proposed pairs in the context of other fe methods found in the literature

ricci flow entropy and optimal transportation let a smooth family of riemannian metrics g tau satisfy the backwards ricer flow equation on a compact oriented n dimensional manifold m suppose two families of normalized n forms omega tau 0 and omega over bar tau 0 satisfy the forwaids in tau heat equation on m generated by the connection laplacian delta g t if these n forms represent two evolving distributions of particles over m the minimum root mean square distance w 2 omega t omega over tilde t t to transport the particles of omega t onto those of omega over tilde t is shown to be non increasing as a function of t without sign conditions on the curvature of mg t moreover this contractivity property is shown to characterize supersolutions to the ricci flow

formulae for the derivatives of heat semigroups abstract formulae for the derivatives of solutions of diffusion equations are derived which clearly exhibit and allow estimation of the equations smoothing properties these also give formulae for the logarithmic gradient of the corresponding heat kernels extending and giving a very elementary proof of bismut s well known formula corresponding formulae are derived for solutions of heat equations for differential forms and their exterior derivatives

heat equation derivative formulas for vector bundles we use martingale methods to give bismut type derivative formulas for differentials and co differentials of heat semigroups on forms and more generally for sections of vector bundles the formulas are mainly in terms of weitzenbock curvature terms in most cases derivatives of the curvature are not involved in particular our results improve b k driver s formula in 1997 j math pures appl 9 76 703 737 for logarithmic derivatives of the heat kernel measure on a riemannian manifold our formulas also include the formulas of k d elworthy and x m li 1998 c r acad sci paris ser i math 327 87 92

integration by parts and quasi invariance for the horizontal wiener measure on foliated compact manifolds abstract we prove several sub riemannian versions of driver s integration by parts formula which first appeared in 17 namely our results are for the horizontal wiener measure on a totally geodesic riemannian foliation equipped with a sub riemannian structure it is also shown that the horizontal wiener measure is quasi invariant under the action of flows generated by suitable tangent processes

a cameron martin type quasi invariance theorem for brownian motion on a compact riemannian manifold abstract let m be a compact manifold without boundary o be a fixed base point in m g be a riemannian metric on m and be a g compatible covariant derivative on tm the tangent space to m assume the torsion t of satisfies the skew symmetry condition g t x y y 0 for all vector fields x and y on m for example take to be the levi civita covariant derivative on m g also let denote the wiener measure on w0 m c 0 1 m 0 o and let h s denote stochastic parallel translation relative to along the path w0 m up to time s 0 1 given a c1 function h 0 1 t0m it is shown that the differential equation t h t h with initial condition 0 id w m w m has a solution r maps w m w m the measurable maps from w m to w m this function is a flow on w m i e for all t r t t furthermore t has the quasi invariance property the law t of t with respect to the wiener measure is equivalent to for all t r this result is used to prove an integration by parts formula for the h derivative hf defined by h f d dt 0 f t where f is a c2 cylinder function on w m

cutoff for the ising model on the lattice introduced in 1963 glauber dynamics is one of the most practiced and extensively studied methods for sampling the ising model on lattices it is well known that at high temperatures the time it takes this chain to mix in l 1 on a system of size n is o logn whether in this regime there is cutoff i e a sharp transition in the l 1 convergence to equilibrium is a fundamental open problem if so as conjectured by peres it would imply that mixing occurs abruptly at c o 1 logn for some fixed c 0 thus providing a rigorous stopping rule for this mcmc sampler however obtaining the precise asymptotics of the mixing and proving cutoff can be extremely challenging even for fairly simple markov chains already for the one dimensional ising model showing cutoff is a longstanding open problem

on gradient bounds for the heat kernel on the heisenberg group it is known that the couple formed by the two dimensional brownian motion and its levy area leads to the heat kernel on the heisenberg group which is one of the simplest sub riemannian space the associated diffusion operator is hypoelliptic but not elliptic which makes difficult the derivation of functional inequalities for the heat kernel however driver and melcher and more recently h q li have obtained useful gradient bounds for the heat kernel on the heisenberg group we provide in this paper simple proofs of these bounds and explore their consequences in terms of functional inequalities including cheeger and bobkov type isoperimetric inequalities for the heat kernel

convergence of mayer expansions the tree graph bound of battle and federbush is extended and used to provide a simple criterion for the convergence of iterated mayer expansions as an application estimates on the radius of convergence of the mayer expansion for the two dimensional yukawa gas nonstable interaction are obtained

log sobolev inequality for the continuum sine gordon model we prove a multiscale generalisation of the bakry emery criterion for a measure to satisfy a log sobolev inequality our criterion relies on the control of an associated pde well known in renormalisation theory the polchinski equation it implies the usual bakry emery criterion but we show that it remains effective for measures which are far from log concave indeed using our criterion we prove that the massive continuum sine gordon model with beta 6 pi satisfies asymptotically optimal log sobolev inequalities for glauber and kawasaki dynamics these dynamics can be seen as singular spdes recently constructed via regularity structures but our results are independent of this theory

hypoelliptic heat kernel inequalities on the heisenberg group we study the existence of l p type gradient estimates for the heat kernel of the natural hypoelliptic laplacian on the real three dimensional heisenberg lie group using malliavin calculus methods we verify that these estimates hold in the case

stochastic analysis on sub riemannian manifolds with transverse symmetries we prove a geometrically meaningful stochastic representation of the derivative of the heat semigroup on sub riemannian manifolds with tranverse symmetries this representation is obtained from the study of bochner weitzenbock type formulas for sub laplacians on 1 forms as a consequence we prove new hypoelliptic heat semigroup gradient bounds under natural global geometric conditions the results are new even in the case of the heisenberg group which is the simplest example of a sub riemannian manifold with transverse symmetries

corrections to sub riemannian geometry an error in the proof of corollary 6 2 of 1 has been pointed out by gerard ben arous the computation of m x in the case o 0 on p 243 is incorrect because m x 0 when 0 0 and jg x 0 for all k there is also a factor of missing in the formula as stated for 0 0 but this is not significant thus when applying the pontryagin theorem theorem 6 1 it is necessary to consider one additional case o 0 and m x9 0 along the curve the conditions of the theorem in this case lead to the equations

log sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality let m be a smooth connected manifold endowed with a smooth measure mu and a smooth locally subelliptic diffusion operator l which is symmetric with respect to mu we assume that l satisfies a generalized curvature dimension inequality as introduced by baudoin garofalo cite bg1 our goal is to discuss functional inequalities for mu like the poincare inequality the log sobolev inequality or the gaussian logarithmic isoperimetric inequality

estimation optimale du gradient du semi groupe de la chaleur sur le groupe de heisenberg abstract en utilisant l inegalite de poincare et la formule de representation on montre que sur le groupe de heisenberg de dimension reelle 3 h 1 il existe une constante c 0 telle que e t f g c e t f g g h 1 t 0 f c o h 1 ce resultat repond par l affirmation a la question ouverte de b k driver t melcher hypoelliptic heat kernel inequalities on the heisenberg group j funct anal 221 2005 340 365 aussi le resultat principal de b k driver t melcher hypoelliptic heat kernel inequalities on the heisenberg group j funct anal 221 2005 340 365 peut etre considere comme une consequence immediate de l inegalite precedente