gibbs measures on brownian currents motivated by applications to quantum field theory we consider gibbs measures for which the reference measure is wiener measure and the interaction is given by a double stochastic integral and a pinning external potential in order properly to characterize these measures through dlr equations we are led to lift wiener measure and other objects to a space of configurations where the basic observables are not only the position of the particle at all times but also the work done by test vector fields we prove existence and basic properties of such gibbs measures in the small coupling regime by means of cluster expansion

a central limit theorem for gibbs measures relative to brownian motion we study a gibbs measure over brownian motion with a pair potential which depends only on the increments assuming a particular form of this pair potential we establish that in the infinite volume limit the gibbs measure can be viewed as brownian motion moving in a dynamic random environment thereby we are in a position to use the technique of kipnis and varadhan and to prove a functional central limit theorem

the evolution of a random vortex filament we study an evolution problem in the space of continuous loops in a three dimensional euclidean space modeled upon the dynamics of vortex lines in 3d incompressible and inviscid fluids we establish existence of a local solution starting from holder regular loops with index greater than 1 3 when the holder regularity of the initial condition x is smaller or equal to 1 2 we require x to be a rough path in the sense of lyons rev mat iberoamericana 14 1998 215 310 system control and rough paths 2002 oxford univ press the solution will then live in an appropriate space of rough paths in particular we can construct local solution starting from almost every brownian loop

probabilistic solution of pauli type equations extends the feynman kac formula to the case of imaginary time schrodinger equations heat equations for multicomponent wavefunctions the approach covers in particular the usual pauli equation for a spin 1 2 particle in an arbitrary magnetic field the formula contains besides the expectation with respect to a wiener process in ordinary space an expectation with respect to a jump process over the discrete indices describing the internal degrees of freedom to illustrate the method the authors evaluate the formula in some special cases and they derive also various inequalities a detailed comparison is made with a recent work by gaveau and vauthier 1981

gibbs measures relative to brownian motion we consider brownian motion perturbed by the exponential of an action the action is the sum of an external one body potential and a two body interaction potential which depends only on the increments under suitable conditions on these potentials we establish existence and uniqueness of the corresponding gibbs measure we also provide an example where uniqueness fails because of a slow decay in the interaction potential

pukanszky s condition and symplectic induction pukanszky s condition is a condition used in obtaining representations from coadjoint orbits in order to obtain more geometric insight in this condition we relate it to symplectic induction it turns out to be equivalent to the condition that the orbit in question is a symplectic subbundle of a modified cotangent bundle

the gibbs ensemble of a vortex filament we introduce a statistical ensemble for a single vortex filament of a three dimensional incompressible fluid the core of the vortex is modeled by a quite generic stochastic process we prove the existence of the partition function for both positive and a limited range of negative temperatures

stochastic analysis rough path analysis and fractional brownian motions in this paper we show by using dyadic approximations the existence of a geometric rough path associated with a fractional brownian motion with hurst parameter greater than 1 4 using the integral representation of fractional brownian motions we furthermore obtain a skohorod integral representation of the geometric rough path we constructed by the results in ly1 a stochastic integration theory may be established for fractional brownian motions and strong solutions and a wong zakai type limit theorem for stochastic differential equations driven by fractional brownian motions can be deduced accordingly the method can actually be applied to a larger class of gaussian processes with covariance functions satisfying a simple decay condition

nonlinear variational formulation for a cavitation problem in lubrication abstract the fluid behaviour in a journal bearing where cavitation takes place is studied this leads to solving a nonlinear variational inequality with normal discontinuity of derivative on a part of the free boundary under some hypotheses using penalization the proof of the existence of a solution is given which is compared with one of a simpler model governed by a classical variational inequality

controlling rough paths abstract we formulate indefinite integration with respect to an irregular function as an algebraic problem which has a unique solution under some analytic constraints this allows us to define a good notion of integral with respect to irregular paths with holder exponent greater than 1 3 e g samples of brownian motion and study the problem of the existence uniqueness and continuity of solution of differential equations driven by such paths we recover young s theory of integration and the main results of lyons theory of rough paths in holder topology

spin boson model through a poisson driven stochastic process we give a functional integral representation of the semigroup generated by the spin boson hamiltonian by making use of a poisson point process and a euclidean field we present a method of constructing gibbs path measures indexed by the full real line which can be applied also to more general stochastic processes with jump discontinuities using these tools we then show existence and uniqueness of the ground state of the spin boson and analyze ground state properties in particular we prove super exponential decay of the number of bosons gaussian decay of the field operators derive expressions for the positive integer fractional and exponential moments of the field operator and discuss the field fluctuations in the ground state

limit behavior of the global solutions to the degasperis procesi type equation abstract in this paper we study the degasperis procesi equation with a physically perturbation term a linear dispersion based on the global existence result we show that the solution of the degasperis procesi equation with linear dispersion tends to the solution of the corresponding degasperis procesi equation as the dispersive parameter goes to zero moreover we prove that smooth solutions of the equation have finite propagation speed they will have compact support if its initial data has this property

central limit theorem for additive functionals of reversible markov processes and applications to simple exclusions we prove a functional central limit theorem for additive functionals of stationary reversible ergodic markov chains under virtually no assumptions other than the necessary ones we use these results to study the asymptotic behavior of a tagged particle in an infinite particle system performing simple excluded random walk

probabilistic models for vortex filaments based on fractional brownian motion we consider a vortex structure based on a three dimensional fractional brownian motion with hurst parameter h 1 2 we show that the energy h has moments of any order under suitable conditions when h 1 2 1 3 we prove that the intersection energy h xy can be decomposed into four terms one of them being a weighted self intersection local time of the fractional brownian motion in r 3

on edwards model for polymer chains ii the self consistent potential we obtain an existence and uniqueness theorem for the self consistent potential in edwards model for polymer chains and confirm the asymptotic analysis proposed by him on the basis of wkb arguments

gibbs measures for brownian paths under the effect of an external and a small pair potential we consider brownian motion in the presence of an external and a weakly coupled pair interaction potential and show that its stationary measure is a gibbs measure uniqueness of the gibbs measure for two cases is shown also the typical path behaviour the degree of mixing and some further properties are derived we use cluster expansion in the small coupling parameter

on the construction of the three dimensional polymer measure the three dimensional polymer measure was first constructed by westwater in 1980 with a very complicated proof we give an alternative construction for small coupling parameter which is based on the approach by brydges frohlich sokal in quantum field theory and bovier felder frohlich using skeleton inequalities the main new features are the proof of convergence which had been open in the brydges frohlich sokal construction and the construction of the measure on the space of paths with fixed time length

global weak solutions and wave breaking phenomena to the periodic degasperis procesi equation with strong dispersion abstract considered herein is the initial value problem for the periodic degasperis procesi equation with a strong dispersive term that is an approximation to the incompressible euler equation for shallow water waves the existence and uniqueness of global weak solutions are established moreover the periodic peakon and shockpeakon solutions of the equation are constructed

functional integral representations of the pauli fierz model with spin 1 2 a feynman kac type formula for a levy and an infinite dimensional gaussian random process associated with a quantized radiation field is derived in particular a functional integral representation of e thpf generated by the pauli fierz hamiltonian with spin 1 2 in non relativistic quantum electrodynamics is constructed when no external potential is applied hpf turns translation invariant and it is decomposed as a direct integral hpf r3 hpf p dp the functional integral representation of e thpf p is also given although all these hamiltonians include spin nevertheless the kernels obtained for the path measures are scalar rather than matrix expressions as an application of the functional integral representations energy comparison inequalities are derived