high density limit theorems for infinite systems of unscaled branching brownian motions the fluctuations of an infinite system of unscaled branching brownian motions in rd are shown to converge weakly under a spatial central limit normalization when the initial density of particles tends to infinity the limit is a generalized gaussian process m which can be written as m mi m where mi is the fluctuation limit of a poisson system of brownian motions obtained by martin lof and mi arises from the spatial central limit normalization of the demographic variation process of the system in the critical case mi and m are independent and m coincides with the generalized ornstein uhlenbeck process found by dawson and by holley and stroock as the renormalization limit of an infinite system of critical branching brownian motions when d 2 3 generalized langevin equations for m mi and m are given

multiscale correlation functions in strong turbulence under the framework of yakhot phys rev e 57 1737 1998 we model intermittent structure functions in fully developed turbulence based on the experimentally supported markovian nature of turbulence cascades friedrich and peinke phys rev lett 78 863 1997 and calculate the multiscaling correlation functions fusion rules l vov and procaccia phys rev lett 76 2898 1996 which were experimentally tested benzi biferale and toschi phys rev lett 80 3244 1998 to be compatible with almost uncorrelated multiplicative process are analytically checked by direct calculations

a particle system with explosions law of large numbers for the density of particles and the blow up time consider a system of independent random walks in the discrete torus with creation annihilation of particles and possible explosion of the total number of particles in finite time rescaling space and rates for diffusion creation annihilation of particles we obtain a strong law of large numbers for the density of particles in the supremum norm the limiting object is a classical solution to the semilinear heat equation t u xx u f u if f u u p 1 p 3 we also obtain a law of large numbers for the explosion time

a law of large numbers for moderately interacting diffusion processes we consider two special models of interacting diffusion processes and derive in the limit as the number of different processes tends to infinity and the interaction is rescaled in a suitable moderate way a law of large numbers for the empirical processes as limit dynamics we obtain certain nonlinear diffusion equations

renormalization group operator product expansion and anomalous scaling in models of turbulent advection recent progress on the anomalous scaling in models of turbulent heat and mass transport is reviewed with the emphasis on the approach based on the field theoretic renormalization group rg and operator product expansion ope in that approach the anomalous scaling is established as a consequence of the existence in the corresponding field theoretic models of an infinite number of dangerous composite fields operators with negative critical dimensions which are identified with the anomalous exponents this allows one to calculate the exponents in a systematic perturbation expansion similar to the e expansion in the theory of critical phenomena the rg and ope approach is presented in a self contained way for the example of a passive scalar field temperature concentration of an impurity etc advected by a self similar gaussian velocity ensemble with vanishing correlation time the so called kraichnan s rapid change model where the anomalous exponents are known up to order o e3 effects of anisotropy compressibility and the correlation time of the velocity field are discussed passive advection by non gaussian velocity field governed by the stochastic navier stokes equation and passively advected vector e g magnetic fields are considered

functional central limit theorem for brownian particles in domains with robin boundary condition abstract we rigorously derive non equilibrium space time fluctuation for the particle density of a system of reflected diffusions in bounded lipschitz domains in r d the particles are independent and are killed by a time dependent potential which is asymptotically proportional to the boundary local time we generalize the functional analytic framework introduced by kotelenez 20 21 to deal with time dependent perturbations our proof relies on dirichlet form method rather than the machineries derived from kotelenez s sub martingale inequality our result holds for any symmetric reflected diffusion for any bounded lipschitz domain and for any dimension d 1

operator space tensor products and inductive limits abstract we investigate whether the tensor product of operator spaces which includes the operator space projective haagerup and schur tensor products and the tensor product of operator systems commute with inductive limits in the sense that if x n n is an inductive system of operator spaces or operator systems with an inductive limit x and if y is any operator space or operator system then whether x n y n id becomes an inductive system and if so whether the inductive limit of this system is same as x y where denotes the tensor product of operator spaces or operator systems we also discuss about the bidual of such an inductive limit and obtain embeddings lim x n y lim x n y under certain restrictions

anomalous scaling nonlocality and anisotropy in a model of the passively advected vector field a model of the passive vector quantity advected by the gaussian velocity field with the covariance ensuremath propto ensuremath delta t ensuremath t ensuremath mathbf x ensuremath mathbf x ensuremath ensuremath varepsilon is studied the effects of pressure and large scale anisotropy are discussed the inertial range behavior of the pair correlation function is described by an infinite family of scaling exponents which satisfy exact transcendental equations derived explicitly in d dimensions by means of the functional techniques the exponents are organized in a hierarchical order according to their degree of anisotropy with the spectrum unbounded from above and the leading minimal exponent coming from the isotropic sector this picture extends to higher order correlation functions like in the scalar model the second order structure function appears nonanomalous and is described by the simple dimensional exponent s 2 ensuremath propto r 2 ensuremath ensuremath varepsilon for the higher order structure functions s 2n ensuremath propto r n 2 ensuremath ensuremath varepsilon ensuremath delta n the anomalous scaling behavior is established as a consequence of the existence in the corresponding operator product expansions of dangerous composite operators whose negative critical dimensions determine the anomalous exponents ensuremath delta n l0 a close formal resemblance of the model with the stirred navier stokes equation reveals itself in the mixing of relevant operators and is the main motivation of the paper using the renormalization group the anomalous exponents are calculated in the o ensuremath varepsilon approximation in large d dimensions for the even structure functions up to the twelfth order

operator space tensor products of c algebras for c algebras a and b the identity map from a widehat otimes b into a otimes b is shown to be injective next we deduce that the center of the completion of the tensor product a b of two c algebras a and b with centers z a and z b under operator space projective norm is equal to z a widehat otimes z b a characterization of isometric automorphisms of a widehat otimes b and a otimes h b is also obtained

spectral synthesis for banach algebras ii this paper continues the study of spectral synthesis and the topologies tau infty and tau r on the ideal space of a banach algebra concentrating particularly on the class of haagerup tensor products of c algebras for this class it is shown that spectral synthesis is equivalent to the hausdorffness of tau infty under a weak extra condition spectral synthesis is shown to be equivalent to the hausdorffness of tau r

comparison methods for a class of function valued stochastic partial differential equations a comparison theorem is derived for a class of function valued stochastic partial differential equations spde s with lipschitz coefficients driven by cylindrical and regular hilbert space valued brownian motions moreover we obtain necessary and sufficient conditions for the positivity of the mild solutions of the spde s where the sufficiency follows from the comparison theorem thereby it is e g possible to identify a class of spde s which can serve as stochastic space time models for the density of particles as a consequence we can construct unique mild solutions of spde s on the cone of positive functions with non lipschitz drift parts including the case of arbitrary polynomialsr x withr o o and leading negative coefficient

limit theorems for age structured populations we study populations consisting of individuals whose birth and death rates depend on both their age and the age structure of the whole population in particular as the population size tends to infinity we derive a law of large numbers and a central limit theorem for the empirical processes

density dependent limits for a nonlinear reaction diffusion model a reaction diffusion model constructed on a grid by linking nonlinear density dependent birth and death processes through particle diffusion is studied by proving two laws of large numbers and a fluctuation theorem under varying assumptions on the density parameter

comparison of stochastic and deterministic models of a linear chemical reaction with diffusion particles placed in n cells on the unit interval give birth or die according to linear rates adjacent cells are coupled by diffusion with a rate proportional to n2 cell numbers are divided by a density parameter to represent concentrations and the resulting space time markov process is compared to a corresponding deterministic model the solution to a partial differential equation the models are viewed as hilbert space valued processes and compared by means of a law of large numbers and central limit theorem new and nearly optimal results are obtained by exploiting the ornstein uhlenbeck type structure of the stochastic model

on the elimination of the sweeping interactions from theories of hydrodynamic turbulence in this paper we revisit the claim that the eulerian and quasi lagrangian same time correlation tensors are equal this statement allows us to transform the results of an msr quasi lagrangian statistical theory of hydrodynamic turbulence back to the eulerian representation we define a hierarchy of homogeneity symmetries between incremental homogeneity and global homogeneity it is shown that both the elimination of the sweeping interactions and the derivation of the 4 5 law require a homogeneity assumption stronger than incremental homogeneity but weaker than global homogeneity the quasi lagrangian transformation on the other hand requires an even stronger homogeneity assumption which is many time rather than one time but still weaker than many time global homogeneity we argue that it is possible to relax this stronger assumption and still preserve the conclusions derived from theoretical work based on the quasi lagrangian transformation

besov spaces and the multifractal hypothesis parisi and frisch proposed some time ago an explanation for multiscaling of turbulent velocity structure functions in terms of a multifractal hypothesis i e they conjecture that the velocity field has local holder exponents in a range hmin hmax with exponents h occurring on a sets h with a fractal dimensiond h heuristic reasoning led them to an expression for the scaling exponentz p ofpth order as the legendre transform of the codimensiond d h we show here that a part of the multifractal hypothesis is correct under even weaker assumptions namely if the velocity field hasl p mean holder indexs i e if it lies in the besov spaceb p s then local holder regularity is satisfied ifs d p then the hypothesis is true in a generalized sense of holder space with negative exponents and we discuss the proper definition of local holder classes of negative index finally if a certain box counting dimension exists then the legendre transform of its codimension gives the scaling exponentz p and more generally the maximal besov index of order p ass p z p p our method of proof is derived from a recent paper of s jaffard using compactly supported orthonormal wavelet bases and gives an extension of his results we discuss implications of the theorems for ensemble average scaling and fluid turbulence

multilocality and fusion rules on the generalized structure functions in two dimensional and three dimensional navier stokes turbulence using the fusion rules hypothesis for three dimensional and two dimensional navier stokes turbulence we generalize a previous nonperturbative locality proof to multiple applications of the nonlinear interactions operator on generalized structure functions of velocity differences we call this generalization of nonperturbative locality to multiple applications of the nonlinear interactions operator multilocality the resulting cross terms pose a new challenge requiring a new argument and the introduction of a new fusion rule that takes advantage of rotational symmetry our main result is that the fusion rules hypothesis implies both locality and multilocality in both the ir and uv limits for the downscale energy cascade of three dimensional navier stokes turbulence and the downscale enstrophy cascade and inverse energy cascade of two dimensional navier stokes turbulence we stress that these claims relate to nonperturbative locality of generalized structure functions on all orders and not the term by term perturbative locality of diagrammatic theories or closure models that involve only two point correlation and response functions

maximal regularity for evolution equations by interpolation and extrapolation on considere le probleme aux valeurs initiales pour l equation d evolution abstraite u t b t u t f t 0 t t ou b t est pour tout t le generateur infinitesimal d un semi groupe analytique dans un b espace e on considere le cas ou le domaine d b t de b t ne depend pas de t

operator space projective tensor product of c algebras for a finite dimensional c algebra a and any c algebra b we determine a constant of equivalence of operator space projective norm cdot wedge and the banach space projective norm cdot gamma on a otimes b we also discuss the banach algebra a widehat otimes b

completely bounded mappings and simplicial complex structure in the primitive ideal space of a c algebra we consider the natural contraction from the central haagerup tensor product of a c algebra a with itself to the space of completely bounded maps cb a on a and investigate those a where there exists an inverse map with finite norm l a we show that a stabilised version l a sup n l m n a depends only on the primitive ideal space prim a the dependence is via simplicial complex structures defined from primal intersections on finite sets of primitive ideals that contain a glimm ideal of a moreover l a l a k h with k h the compact operators which requires us to develop the theory in the context of c algebras that are not necessarily unital

linear parabolic differential equations as limits of space time jump markov processes abstract a class of linear parabolic differential equations on a bounded domain in rn is obtained as the class of deterministic limits of space time jump markov processes xn these xn describe particle systems which are spatially inhomogeneous due to diffusion and random change in the number of particles the deviation of xn from its deterministic limit is measured by a central limit theorem this fluctation limit is a distribution valued generalized ornstein uhlenbeck process and can be represented as the mild solution of a stochastic partial differential equation whose driving term is the sum of two independent gaussian martingales arising from diffusion and change in the number of particles respectively

langevin equations for l valued gaussian processes and fluctuation limits of infinite particle systems l gaussian processes of a certain class are shown to satisfy generalized langevin equations examples are fluctuation limits of several infinite particle systems in particular infinite particle branching brownian motions with immigration under various scalings and the voter model with hydrodynamic scaling

local operator multipliers and positivity we establish an unbounded version of stinespring s theorem and a lifting result for stinespring representations of completely positive modular maps defined on the space of all compact operators we apply these results to study positivity for schur multipliers we characterise positive local schur multipliers and provide a description of positive local schur multipliers of toeplitz type we introduce local operator multipliers as a non commutative analogue of local schur multipliers and characterise them extending both the characterisation of operator multipliers from 16 and that of local schur multipliers from 27 we provide a description of the positive local operator multipliers in terms of approximation by elements of canonical positive cones

on the derivation of reaction diffusion equations as limit dynamics of systems of moderately interacting stochastic processes we consider systems of moderately interacting particles which are divided into a finite number of different subpopulations and show that in the limit as the population size tends to infinity the empirical processes of the subpopulations converge to the solution of a system of reaction diffusion equations

convergence of s valued processes and space time random fields abstract the mapping x x of d 0 t s r d into s r d 1 defined by x 0 t x t t dt s r d 1 is shown to be continuous this is used to prove that for a tight sequence of processes x n inn in d 0 t s r d weak convergence of x n n in s r d 1 implies weak convergence of x n when 0 t is replaced by 0 the space s r d 1 is not appropriate in general and we investigate the question of what is the smallest nuclear space of distributions containing s r d 1 that can be used our motivation comes from the asymptotic analysis of particle systems

a fluctuation theorem for moderately interacting diffusion processes we study the asymptotic behaviour of the fluctuations of the empirical processes of the second example of moderately interacting diffusion processes of 3 and show that in the limit as the number of different processes tends to infinity these fluctuations behave gaussian

spectral synthesis and topologies on ideal spaces for banach algebras this paper continues the study of spectral synthesis and the topologies and r on the ideal space of a banach algebra concentrating on the class of banach algebras and in particular on l1 group algebras it is shown that if a group g is a finite extension of an abelian group then r is hausdorff on the ideal space of l1 g if and only if l1 g has spectral synthesis which in turn is equivalent to g being compact the result is applied to nilpotent groups fd groups and moore groups an example is given of a non compact non abelian group g for which l1 g has spectral synthesis it is also shown that if g is a non discrete group then r is not hausdorff on the ideal lattice of the fourier algebra a g

systems of interacting diffusions with partial annihilation through membranes we introduce an interacting particle system in which two families of reflected diffusions interact in a singular manner near a deterministic interface ii this system can be used to model the transport of positive and negative charges in a solar cell or the population dynamics of two segregated species under competition a related interacting random walk model with discrete state spaces has recently been introduced and studied in chen and fan 2014 in this paper we establish the functional law of large numbers for this new system thereby extending the hydrodynamic limit in chen and fan 2014 to reflected diffusions in domains with mixed type boundary conditions which include absorption harvest of electric charges we employ a new and direct approach that avoids going through the delicate bbgky hierarchy

high density limit theorems for nonlinear chemical reactions with diffusion the solutionx of a nonlinear reaction diffusion equation on then dimensional unit cubes is approximated by a space time jump markov processx v n law of large numbers lln x v n is constructed on a grids n ons ofn cells wherev is proportional to the initial number of particles in each cell the deviation ofx v n fromx is computed by a central limit theorem clt the assumptions on the parametersv n are for the lln asn and for the clt frac n upsilon to 0 asn the limity y x in the clt which is a generalized ornstein uhlenbeck process is represented as the mild solution of a linear stochastic partial differential equation spde and its best possible state spaces are described the problem of stationary solutions ofy x in dependence ofx is also investigated