the twisting trick for double well hamiltonians we show that the use of a twisting trick allows a transparent geometrical analysis of the spectral properties of double well hamiltonians in particular one can provenorm resolvent convergence of the relevant hamiltonians whenever one has two centres of force whose separationr diverges to infinity

semiclassical analysis of low lying eigenvalues iv the flea on the elephant abstract the two lowest eigenvalues e 0 e 1 of a symmetric double well tunnelling problem 2 v as are considered and they are compared to the two lowest eigenvalues e 0 e 1 of 2 v w where w is supported away from the well bottoms of v we determine the leading exponential splitting of various differences of the four numbers e 0 e 1 e 0 e 1 related problems are discussed

global boundary centric feature extraction and associated discontinuity metrics portions from time domain speech segments are extracted feature vectors that represent the portions in a vector space are created the feature vectors incorporate phase information of the portions a distance between the feature vectors in the vector space is determined in one aspect the feature vectors are created by constructing a matrix w from the portions and decomposing the matrix w in one aspect decomposing the matrix w comprises extracting global boundary centric features from the portions in one aspect the portions include at least one pitch period in another aspect the portions include centered pitch periods

numerical analysis for a macroscopic model in micromagnetics the macroscopic behavior of stationary micromagnetic phenomena can be modeled by a relaxed version of the landau lifshitz minimization problem in the limit of large and soft magnets omega it is reasonable to exclude the exchange energy and convexify the remaining energy densities the numerical analysis of the resulting minimization problem begin align min e 0 bf m text amongst bf m omega to mathbb r d text with bf m x le1 text for almost every x in omega end align for d 2 3 faces difficulties caused by the pointwise side constraint bf m le1 and an integral over the whole space mathbb r d for the stray field energy this paper involves a penalty method to model the side constraint and reformulates the exterior maxwell equation via a nonlocal integral operator mathcal p acting on functions exclusively defined on omega the discretization with piecewise constant discrete magnetizations leads to edge oriented boundary integrals the implementation of which and related numerical quadrature are discussed as are adaptive algorithms for automatic mesh refinement a priori and a posteriori error estimates provide a thorough rigorous error control of certain quantities three classes of numerical experiments study the penalization empirical convergence rates and performance of the uniform and adaptive mesh refining algorithms

semiclassical analysis of low lying eigenvalues ii tunneling we discuss the leading asymptotics of eigenvalue splittings of 2 x2v in the limit as x o and where v is a non negative potential with several zeros for example if eo x e1 x are the two lowest eigenvalues in a situation where v has precisely two zeros a and b related by a symmetry then limx x lin e1 x eo x is given as the distance from a to b in a certain riemann metric

sobolev spaces and capacities theory on path spaces over a compact riemannian manifold we introduce sobolev spaces and capacities on the path space p m 0 m over a compact riemannian manifold m we prove the smoothness of the ito map and the stochastic anti development map in the sense of stochastic calculus of variation we establish a sobolev norm comparison theorem and a capacity comparison theorem between the wiener space and the path space p m 0 m moreover we prove the tightness of r p capacities on p m 0 m which generalises a result due to airault malliavin and sugita on the wiener space finally we extend our results to the fractional holder continuous path space

splitting in large dimension and infrared estimates ii moment inequalities this is the continuation of notes written for the nato asi conference in il ciocco september 96 consisting of the analysis of the links between estimating the splitting between the two first eigenvalues for the schrodinger operator h and the proof of infrared estimates for quantities attached to gaussian type measures these notes were mainly reporting on the old contributions of dyson frohlich glimm jaffe lieb simon and spencer in the 1970s in connection with more recent contributions of pastur khoruzhenko barbulyak and kondrat ev which treat in general more sophisticated models here we concentrate on the simplest model related to field theory and extend the results of barbulyak and kondrat ev by mixing ideas coming from pastur and khozurenko related to the use of bogolyubov s inequality with classical inequalities due to ginibre lebowitz sokal and others or in the case when the temperature t is zero by applying rather elementary estimates on schrodinger operators in order to find

method of and device for segmenting an electric signal derived from an acoustic signal a method and device for segmenting an electric acoustic signal a number of parameters for example log area parameters are derived as a function of time from the electric signal block 2 for consecutive instants the signals of the parameters located within a time interval around each instant are taken up and transition functions 0 i are derived therefrom for each instant block 3 subsequently similarity factors c ij are determined each between two transition functions 0 i and 0 j associated with respective proximate instants i and j block 4 and a replacing transition function 0 ij c is derived block 6 from the transition functions of at least one group of two transition functions for which the associated similarity factor is larger than a reference value v the transition function 0 ij c replace the aforementioned transition functions from which it is derived block 7 a combined transition function 0 ij c replacing one of these transition functions is preferably calculated from the aforementioned transition functions while the other of these transition functions are omitted the group of transition functions for which the similarity factor is largest is preferably taken block 5 the method is subsequently repeated fig 1 transition functions obtained are very suitable for use in the transmission or recognition of speech signals and for coding diphones

semiclassical asymptotics of eigenvalues for schrodinger operators with magnetic fields abstract we consider schrodinger operators with magnetic fields on a two dimensional compact manifold or on r 2 the purpose is to study the semiclassical asymptotics of the eigenvalues by two different methods we obtain some facts on the harmonic oscillators under uniform magnetic fields and we also discuss them

weak poincare inequalities on domains defined by brownian rough paths we prove weak poincare inequalities on domains which are inverse images of open sets in wiener spaces under continuous functions of brownian rough paths the result is applicable to dirichlet forms on loop groups and connected open subsets of path spaces over compact riemannian manifolds

new approach to the semiclassical limit of quantum mechanics i multiple tunnelings in one dimension we propose a new approach for the estimate of the rate of degeneracy of the lowest eigenvalues of the schrodinger operator in the presence of tunneling based on the theory of diffusion processes our method provides lower and upper bounds for the energy splittings and the rates of localization of the wave functions and enables us to discuss cases which as far as we know have never been treated rigorously in the literature in particular we give an analysis of the effect on eigenvalues and eigenfunctions of localized deformations of 1 symmetric double well potentials 2 potentials periodic and symmetric over a finite interval theses situations are characterized by a remarkable dependence on such deformations our probabilistic techniques are inspired by the theory of small random perturbations of dynamical systems

trace formulas a golden thompson inequality and classical limit in boson fock space trace formulas for the heat semi groups of second quantization operators and their perturbations in the abstract boson fock space are given in terms of path functional integral representations as applications an inequality of golden thompson type and a classical limit are derived for the trace of the heat semi group of a perturbed second quantization operator the abstract results are applied to a model ofp type in quantum field theory

supersymmetry and morse theory it is shown that the morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics hamiltonian some of the implications of modern ideas in mathematics for supersymmetric theories are discussed

boundary lagrange multipliers in finite element methods error analysis in natural norms a finite element procedure for circumventing the babuska brezzi condition in mixed formulations with lagrange multipliers defined on the boundary is presented residual terms constructed from the euler lagrange equations are added to the classical galerkin formulation in order to attain coercivity in a mesh dependent norm convergence is proven for the primal variable and the multiplier in the natural mesh independent norm of the problem generalizing results of a previous paper

spectral and scattering theory of spatially cut off p ϕ 2 hamiltonians we study spatially cut off p 2 hamiltonians we show the local finiteness of the pure point spectrum outside of thresholds the limiting absorption principle and asymptotic completeness of scattering for such hamiltonians our results imply the absence of singular continuous spectrum

logarithmic sobolev inequalities on loop groups let g be a compact lie group denote by m the brownian bridge measure on the loop group y g c 0 1 g g 0 g 1 e the finite energy subgroup of y determines in a natural way a gradient operation for functions on y the following logarithmic sobolev inequality is proven f2 log f dm gradf y 2 v y f y 2 dm f 2log f wherein f denotes the l2 m norm and v is a potential which is quadratic in the associated lie algebra valued brownian motion the inequality is derived by a method of inheritance from the known inequality for the g valued brownian motion

finite dimensional approximations to wiener measure and path integral formulas on manifolds abstract certain natural geometric approximation schemes are developed for wiener measure on a compact riemannian manifold these approximations closely mimic the informal path integral formulas used in the physics literature for representing the heat semi group on riemannian manifolds the path space is approximated by finite dimensional manifolds h p m consisting of piecewise geodesic paths adapted to partitions p of 0 1 the finite dimensional manifolds h p m carry both an h 1 and a l 2 type riemannian structures g 1 p and g 0 p respectively it is proved that 1 z i p e 1 2 e d vol g i p i d as mesh p 0 where e is the energy of the piecewise geodesic path h p m and for i 0 and 1 z i p is a normalization constant vol g i p is the riemannian volume form relative to g i p and is wiener measure on paths on m here 1 1 and 0 exp 1 6 1 0 scal s ds where scal is the scalar curvature of m these results are also shown to imply the well known integration by parts formula for the wiener measure

krein s formula and one dimensional multiple well abstract it is shown that all the discrete eigenvalues of a one dimensional schrodinger operator with a multiple well potential possess an asymptotic expansions in power of h 1 2 when h 0 a formula for all the coefficients of these expansions is given the method uses two main tools perturbation by boundary conditions and exponential decay of eigenfunctions which are developed in this article as a by product of this work the exponential localization of eigenvectors when h goes to zero can be proved

logarithmic sobolev inequalities and exponential integrability we prove the exponential integrability of lipschitz functions in abstract wiener spaces by using logarithmic sobolev inequalities we introduce two notions of lipschitz continuity and apply the method of davis and simon j funct anal 59 1984 335 395 to prove our main theorem moreover we give several conditions under which the function is exponentially integrable

semi classical limit of the lowest eigenvalue of a schrodinger operator on a wiener space ii p ϕ 2 model on a finite volume abstract we determine the semi classical limit of the lowest eigenvalue of a p 2 hamiltonian on a finite volume interval

laplace s method for the laws of heat processes on loop spaces abstract in this paper we will consider laplace s method for a class of heat processes on loop spaces we will obtain the first term of the asymptotics under assumptions that the function under consideration attains its minimum at a unique point and that the hessian at the point is non degenerate this kind of process was first introduced by p malliavin in 1990 for the loop group case and then gradually generalized by various authors our tool is the rough path theory of t lyons this technique was pioneered by s aida for finite dimensional processes in his unpublished paper

critical friction for wedged configurations abstract a wedged configuration with coulomb friction is a nontrivial equilibrium state of a linear elastic body in a frictional unilateral contact with a rigid body under vanishing external loads we analyze here the relation between the geometry of the elastic body and the friction coefficient for which wedged configurations exist in a 3 d context the critical friction coefficient w is defined as the infimum of a supremal functional defined on the set of admissible normal displacement and tangential stresses for friction coefficients with w the wedged problem has at least a solution and for the wedged problem is stated in a discrete framework using a mixed finite element approach and the discrete critical friction coefficient h w is introduced as the solution of a global minimization problem involving a non differentiable and non convex functional the existence of h the displacement field of a critical wedged state is proved and a specific numerical method based on a genetic algorithm was developed to compute the critical wedged configurations some techniques to handle the discontinuities of the normal vector on the contact surface are presented and the analysis is illustrated with three numerical simulations

tunneling for spatially cut off p phi _2 hamiltonians we study the asymptotic behavior of low lying eigenvalues of spatially cut off p 2 hamiltonian in the semi classical limit we determine the semi classical limit of the lowest eigenvalue of the hamiltonian in terms of the hessian of the potential function of the corresponding classical equation moreover we prove that the gap of the lowest two eigenvalues goes to 0 exponentially fast in the semi classical limit when the potential function is double well type in fact we prove that the exponential decay rate is greater than or equal to the agmon distance between two zero points of the symmetric double well potential function also we study basic properties of the agmon distance and instanton

semiclassical limit of the lowest eigenvalue of a schrodinger operator on a wiener space abstract we study a semiclassical limit of the lowest eigenvalue of a schrodinger operator on a wiener space key results are semiboundedness theorem of the schrodinger operator laplace type asymptotic formula and ims localization formula we also make a remark on the semiclassical problem of a schrodinger operator on a path space over a riemannian manifold

data driven global boundary optimization portions from segment boundary regions of a plurality of speech segments are extracted each segment boundary region is based on a corresponding initial unit boundary feature vectors that represent the portions in a vector space are created for each of a plurality of potential unit boundaries within each segment boundary region an average discontinuity based on distances between the feature vectors is determined for each segment the potential unit boundary associated with a minimum average discontinuity is selected as a new unit boundary

witten s complex and infinite dimensional morse theory we investigate the relation between the trajectories of a finite dimensional gradient flow connecting two critical points and the cohomology of the surrounding space the results are applied to an infinite dimensional problem involving the symplect c action function

the log sobolev inequality on loop space over a compact riemannian manifold abstract we obtain a log sobolev inequality with a neat and explicit potential for the gradient on a based loop space over a compact riemannian manifold the potential term relies only on the curvature of the manifold and the hessian of the heat kernel and is l p integrable for all p 1 the log sobolev inequality is derived by a martingale representation theorem for the differentiable functions on loop space which is a variation of the clark ocone haussmann formula

on the spectrum of semi classical witten laplacians and schrodinger operators in large dimension we investigate the low lying spectrum of witten laplacians on forms of arbitrary degree in the semi classical limit and uniformly in the space dimension we show that under suitable assumptions implying that the phase function has a unique local minimum one obtains a number of clusters of discrete eigenvalues at the bottom of the spectrum moreover we are able to count the number of eigenvalues in each cluster we apply our results to certain sequences of schrodinger operators having strictly convex potentials and show that some well known results of semi classical analysis hold also uniformly in the dimension

a priori and a posteriori error analysis for a large scale ocean circulation finite element model we consider the finite element solution of the stream function vorticity formulation for a large scale ocean circulation model first we study existence and uniqueness of solution for the continuous and discrete problems under appropriate regularity assumptions we prove that the stream function can be computed with an error of order h in h1 seminorm second we introduce and analyze an h adaptive mesh refinement strategy to reduce the spurious oscillations and poor resolution which arise when convective terms are dominant we propose an a posteriori anisotropic error indicator based on the recovery of the hessian from the finite element solution which allows us to obtain well adapted meshes the numerical experiments show an optimal order of convergence of the adaptive scheme furthermore this strategy is efficient to eliminate the oscillations around the boundary layer

fem bem coupling for the large body limit in micromagnetics we present and analyze a coupled finite element boundary element method for a model in stationary micromagnetics the finite element part is based on mixed conforming elements for two and three dimensional settings we show well posedness of the discrete problem and present an a priori error analysis for the case of lowest order elements

parallel domain decomposition procedures of improved d d type for parabolic problems two parallel domain decomposition procedures for solving initial boundary value problems of parabolic partial differential equations are proposed one is the extended d d type algorithm which extends the explicit implicit conservative galerkin domain decomposition procedures given in 5 from a rectangle domain and its decomposition that consisted of a stripe of sub rectangles into a general domain and its general decomposition with a net like structure an almost optimal error estimate without the factor h 1 2 given in dawson dupont s error estimate is proved another is the parallel domain decomposition algorithm of improved d d type in which an additional term is introduced to produce an approximation of an optimal error accuracy in l 2 norm

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

leading large order asymptotics for φ4 2 perturbation theory we develop a rigorous semiclassical expansion to compute the radius of convergence of the borel transform for the pressure in 4 2 field theory this result gives a partial justification for the lipatov method of finding large order perturbation theory asymptotics in quantum field theory

an approximation to wiener measure and quantization of the hamiltonian on manifolds with non positive sectional curvature this paper gives a rigorous interpretation of a feynman path integral on a riemannian manifold m with non positive sectional curvature an l2 riemannian metric gp is given on the space of piecewise geodesic paths hp m adapted to the partition p of 0 1 whence a finite dimensional approximation of wiener measure is developed it is proved that as mesh p 0 the approximate wiener measure converges in an l1 sense to the measure exp 2 3203 01scal s ds d on the wiener space w m with wiener measure this gives a possible prescription for the path integral representation of the quantized hamiltonian as well as yielding such a result for the natural geometric approximation schemes originating in andersson and driver 1999 3 and followed by lim 2007 34

domain decomposition based mathcal h lu preconditioning hierarchical matrices provide a data sparse way to approximate fully populated matrices the two basic steps in the construction of an mathcal h matrix are a the hierarchical construction of a matrix block partition and b the blockwise approximation of matrix data by low rank matrices in this paper we develop a new approach to construct the necessary partition based on domain decomposition compared to standard geometric bisection based mathcal h matrices this new approach yields mathcal h lu factorizations of finite element stiffness matrices with significantly improved storage and computational complexity requirements these rigorously proven and numerically verified improvements result from an mathcal h matrix block structure which is naturally suited for parallelization and in which large subblocks of the stiffness matrix remain zero in an lu factorization we provide numerical results in which a domain decomposition based mathcal h lu factorization is used as a preconditioner in the iterative solution of the discrete three dimensional convection diffusion equation

semi classical limit of the bottom of spectrum of a schrodinger operator on a path space over a compact riemannian manifold abstract we determine the limit of the bottom of spectrum of schrodinger operators with variable coefficients on wiener spaces and path spaces over finite dimensional compact riemannian manifolds in the semi classical limit these are extensions of the results in s aida semiclassical limit of the lowest eigenvalue of a schrodinger operator on a wiener space j funct anal 203 2 2003 401 424 the problem on path spaces over riemannian manifolds is considered as a problem on wiener spaces by using ito s map however the coefficient operator is not a bounded linear operator and the dependence on the path is not continuous in the uniform convergence topology if the riemannian curvature tensor on the underling manifold is not equal to 0 the difficulties are solved by using unitary transformations of the schrodinger operators by approximate ground state functions and estimates in the rough path analysis

logarithmic sobolev inequalities on path spaces over riemannian manifolds let w o m be the space of paths of unit time length on a connected complete riemannian manifold m such that 0 o a fixed point on m and the wiener measure on w o m the law of brownian motion on m starting at o if the ricci curvature is bounded by c then the following logarithmic sobolev inequality holds

on the ornstein uhlenbeck operators on wiener riemannian manifolds abstract in this paper we study the properties of infinite dimensional ornstein uhlenbeck operators on submanifolds in wiener spaces we establish the hypoellipticity of the laplacians acting on the space of tensors by using this we show the essential selfadjointness of the laplacians acting on the space of 0 forms i e function spaces

precise asymptotics of certain wiener functionals abstract in this article we present a method for developing certain wiener integrals in an asymptotic expansion as the variance of the wiener goes to 0 the basic ideas are a combination of methods borrowed from the theory of large deviations together with techniques from the calculus of wiener space

inverse inequalities on non quasi uniform meshes and application to the mortar element method we present a range of mesh dependent inequalities for piecewise constant and continuous piecewise linear finite element functions u defined on locally refined shape regular but possibly non quasi uniform meshes these inequalities involve norms of the form h u w s p for positive and negative s and where h is a function which reflects the local mesh diameter in an appropriate way the only global parameter involved is n the total number of degrees of freedom in the finite element space and we avoid estimates involving either the global maximum or minimum mesh diameter our inequalities include new variants of inverse inequalities as well as trace and extension theorems they can be used in several areas of finite element analysis to extend results previously known only for quasi uniform meshes to the locally refined case here we describe applications to i the theory of nonlinear approximation and ii the stability of the mortar element method for locally refined meshes

discrete boundary element methods on general meshes in 3d abstract this paper is concerned with the stability and convergence of fully discrete galerkin methods for boundary integral equations on bounded piecewise smooth surfaces in mathbb r 3 our theory covers equations with very general operators provided the associated weak form is bounded and elliptic on h mu for some mu in 1 1 in contrast to other studies on this topic we do not assume our meshes to be quasiuniform and therefore the analysis admits locally refined meshes to achieve such generality standard inverse estimates for the quasiuniform case are replaced by appropriate generalised estimates which hold even in the locally refined case since the approximation of singular integrals on or near the diagonal of the galerkin matrix has been well analysed previously this paper deals only with errors in the integration of the nearly singular and smooth galerkin integrals which comprise the dominant part of the matrix our results show how accurate the quadrature rules must be in order that the resulting discrete galerkin method enjoys the same stability properties and convergence rates as the true galerkin method although this study considers only continuous piecewise linear basis functions on triangles our approach is not restricted in principle to this case as an example the theory is applied here to conventional triangle based quadrature rules which are commonly used in practice a subsequent paper 14 introduces a new and much more efficient node based approach and analyses it using the results of the present paper

numerical quadratic energy minimization bound to convex constraints in thin film micromagnetics we analyze the reduced model for thin film devices in stationary micromagnetics proposed in desimone et al r soc lond proc ser a math phys eng sci 457 2016 2983 2991 2001 we introduce an appropriate functional analytic framework and prove well posedness of the model in that setting the scheme for the numerical approximation of solutions consists of two ingredients the energy space is discretized in a conforming way using raviart thomas finite elements the non linear but convex side constraint is treated with a penalty method this strategy yields a convergent sequence of approximations as discretization and penalty parameter vanish the proof generalizes to a large class of minimization problems and is of interest beyond the scope of thin film micromagnetics

renormalized differential geometry on path space structural equation curvature abstract the theory of integration in infinite dimensions is in some sense the backbone of probability theory on this backbone the stochastic calculus of variations has given rise to the flesh of differential calculus its first step is the construction at each point of the probability space of a cameron martin like tangent space in which the desired differential calculus can be developed this construction proceeds along the lines of first order differential geometry in this paper we address the following questions what could be the meaning of curvature of the probability space how and why how can curvatures be defined and computed why could a second order differential geometry be relevant to stochastic analysis we try to answer these questions for the probability space associated to the brownian motion of a compact riemannian manifold why a basicenergy identity for anticipative stochastic integralswill be obtained as a byproduct of our computation of curvature how there are essentially four bottlenecks in the development of differential geometry on wiener riemann manifolds i the difficulty of finding an atlas of local charts such that the changes of charts preserve the class of the wiener like measures together with their associated cameron martin like tangent spaces ii the difficulty of finding cylindrical approximations preserving the natural geometrical objects iii the difficulty of renormalizing the divergent series to which the summation operations of finite dimensional differential geometry give rise in the non intrinsic context of local charts iv the nonavailability of the computational procedures analogous to the local coordinates systems of the classical differential geometry in the context of path space the ito filtration provides a much richer structure than that available in the framework of an abstract wiener riemann manifold our work is a systematic attempt to replace the machinery of local charts with amethodology of moving frames in our context stochastic parallel transport provides a canonical moving frame on the path space the concept of a cylindrical approximation has to be reshaped in our new situation into some geometric limit theorems establishing that the riemannian geometric objects of the cylindrical approximations induce by a limiting procedure geometric objects on the path space those limit theorems are reminiscent of the classical theorems which say that a stratonovich sde is the limit of an appropriate sequence of ode the canonical coordinate system provided by the moving frame will make it possible to proceed to the needed renormalizations byintrinsicstochastic integrals in this context the anticipative stochastic integral theory of nualart and pardoux will play a decisive role finally the moving frame will provide aneffective algorithm of computation for this differential geometry in infinite dimensions in our study we encounter a new type of renormalization thehypoelliptic renormalization which corresponds to the fact that the bracket of smooth vector fields taking their values in the cameron martin space can get out of this cameron martin space this hypoelliptic problem induces the nonrenormalizability of some geometrical objects it leads also to a concept oftangent processesto probability spaces extending that based on the cameron martin theorem for tangent processes a formula of integration by parts still holds furthermore the tangent processes form a lie algebra under the bracket on the other hand tangent processes cannot be stochastically integrated this operation is well defined only for cameron martin type vector fields

asymptotic expansions for the laplace approximations for ito functionals of brownian rough paths abstract in this paper we establish asymptotic expansions for the laplace approximations for ito functionals of brownian rough paths under the condition that the phase function has finitely many non degenerate minima our main tool is the banach space valued rough path theory of t lyons we use a large deviation principle and the stochastic taylor expansion with respect to the topology of the space of geometric rough paths this is a continuation of a series of papers by inahama y inahama laplace s method for the laws of heat processes on loop spaces j funct anal 232 2006 148 194 and by inahama and kawabi y inahama h kawabi large deviations for heat kernel measures on loop spaces via rough paths j london math soc 73 3 2006 797 816 y inahama h kawabi on asymptotics of certain banach space valued ito functionals of brownian rough paths in proceedings of the abel symposium 2005 stochastic analysis and applications a symposium in honor of kiyosi ito springer berlin in press available at http www abelprisen no no abelprisen deltagere 2005 html

the double well splitting of the low energy levels for the schrodinger operator of discrete φ4 models on tori the formula is obtained for the asymptotics of the splitting of the first two eigenvalues of the schrodinger operator that stands for the discrete multidimensional 4 model on tori the behavior of the main term is investigated in the limit of the large number of particles

asymptotics of spectral gaps on loop spaces over a class of riemannian manifolds abstract we prove the existence of spectral gaps of ornstein uhlenbeck operators on loop spaces over a class of riemannian manifolds which include hyperbolic spaces this is an alternative proof and an extension of a result in chen et al 13 further we study the asymptotic behavior of the spectral gap

numerical analysis of relaxed micromagnetics by penalised finite elements some micromagnetic phenomena in rigid ferro magnetic materials can be modelled by a non convex minimisation problem typically minimising sequences develop finer and finer oscillations and their weak limits do not attain the infimal energy solutions exist in a generalised sense and the observed microstructure can be described in terms of young measures a relaxation by convexifying the energy density resolves the essential macroscopic information the numerical analysis of the relaxed problem faces convex but degenerated energy functionals in a setting similar to mixed finite element formulations the lowest order conforming finite element schemes appear instable and nonconforming finite element methods are proposed an a priori and a posteriori error analysis is presented for a penalised version of the side restriction that the modulus of the magnetic field is bounded pointwise residual based adaptive algorithms are proposed and experimentally shown to be efficient

an estimate of the gap of spectrum of schrodinger operators which generate hyperbounded semigroups abstract logarithmic sobolev inequalities with potential functions on loop spaces were proved by l gross 1991 j funct anal 102 265 313 s aida 1996 in proceedings of the fifth gregynog symposium stochastic analysis and applications pp 1 19 world scientific singapore and f z gong and z m ma 1998 j funct anal 599 623 the generators of the dirichlet forms are schrodinger operators on loop spaces and they generate hyperbounded semigroups recently f z gong m rockner and l m wu 2000 poincare inequality for weighted first order sobolev spaces on loop spaces submitted proved the existence of the gap of spectrum at the lowest eigenvalue of the schrodinger operators by using m hino s exponential decay estimates of the semigroup 2000 osaka j math 37 603 624 and the author s strong ergodicity property of the semi group s aida 1998 j funct anal 158 152 185 in this paper we will give a lower bound on the gap by using a weak poincare inequality which was introduced by m rockner and f y wang 2000 weak poincare inequalities and l 2 convergence rates of markov semigroups preprint also we will give estimates on the distribution function of ground states using the weak poincare inequality