rigidity and tolerance in point processes gaussian zeros and ginibre eigenvalues let be a translation invariant point process on the complex plane c and let d c be a bounded open set we ask the following what does the point configuration out obtained by taking the points of outside d tell us about the point configuration in of inside d we show that for the ginibre ensemble out determines the number of points in in for the translation invariant zero process of a planar gaussian analytic function we show that out determines the number as well as the center of mass of the points in in further in both models we prove that the outside says nothing more about the inside in the sense that the conditional distribution of the inside points given the outside is mutually absolutely continuous with respect to the lebesgue measure on its supporting submanifold

invariant palm and related disintegrations via skew factorization let g be a measurable group with haar measure acting properly on a space s and measurably on a space t then any finite jointly invariant measure m on s t admits a disintegration nu otimes mu into an invariant measure on s and an invariant kernel from s to t here we construct and by a general skew factorization which extends an approach by rother and zahle for homogeneous spaces s over g this leads to easy extensions of some classical propositions for invariant disintegration previously known in the homogeneous case the results are applied to the palm measures of jointly stationary pairs where is a random measure on s and is a random element in t

invariant measures and disintegrations with applications to palm and related kernels consider a locally compact group g acting measurably on some spaces s and t we prove a general representation of g invariant measures on s and the existence of invariant disintegrations of jointly invariant measures on s t the results are applied to palm and related kernels associated with a stationary random pair where is a random measure on s and is a random element in t

skorokhod embeddings for two sided markov chains let x n n in mathbb z be a two sided recurrent markov chain with fixed initial state x 0 and let nu be a probability measure on its state space we give a necessary and sufficient criterion for the existence of a non randomized time t such that x t n n in mathbb z has the law of the same markov chain with initial distribution nu in the case when our criterion is satisfied we give an explicit solution which is also a stopping time and study its moment properties we show that this solution minimizes the expectation of psi t in the class of all non negative solutions simultaneously for all non negative concave functions psi

a coarse grid projection method for accelerating incompressible flow computations we present a coarse grid projection cgp method for accelerating incompressible flow computations which is applicable to methods involving poisson equations as incompressibility constraints the cgp methodology is a modular approach that facilitates data transfer with simple interpolations and uses black box solvers for the poisson and advection diffusion equations in the flow solver after solving the poisson equation on a coarsened grid an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid a particular version of the method is applied here to the vorticity stream function primitive variable and vorticity velocity formulations of incompressible navier stokes equations we compute several benchmark flow problems on two dimensional cartesian and non cartesian grids as well as a three dimensional flow problem the method is found to accelerate these computations while retaining a level of accuracy close to that of the fine resolution field which is significantly better than the accuracy obtained for a similar computation performed solely using a coarse grid a linear acceleration rate is obtained for all the cases we consider due to the linear cost elliptic poisson solver used with reduction factors in computational time between 2 and 42 the computational savings are larger when a suboptimal poisson solver is used we also find that the computational savings increase with increasing distortion ratio on non cartesian grids making the cgp method a useful tool for accelerating generalized curvilinear incompressible flow solvers

transforming random elements and shifting random fields consider a locally compact second countable topological transformation group acting measurably on an arbitrary space we show that the distributions of two random elements x and x in this space agree on invariant sets if and only if there is a random transformation r such that rx has the same distribution as x applying this to random fields in d dimensions under site shifts we show further that these equivalent claims are also equivalent to site average total variation convergence this convergence result extends to amenable groups

refined interaction method for direct numerical simulation of transition in separation bubbles in direct numerical simulations dns of laminar turbulent transition in laminar separation bubbles the definition of a well posed freestream boundary condition is crucial different partially contradicting properties are required e rst an adverse pressure gradient has to be imposed to force separation moreover oscillations at the freestream boundary caused by disturbance waves which extend into the potential e ow have to be treated accurately finally displacement effects of the separation bubble on the surrounding potential e ow by the so called viscous inviscid boundary layer interaction have to be captured usually either the integration domain has to be sufe ciently high or a state of the art boundary layer interaction model based on the theory of thin airfoils can be applied at a high reynolds number at separation neither possibility is applicable therefore an improved model has been developed that meets the just mentioned requirements the method is validated by variations of the height of the integration domain it is shown that boundary layer interaction has not only quantitative but even qualitative impact on the separation bubble the comparison of a highly resolved dns with an experiment proves the applicability of the present method for separation bubbles on airfoils nomenclature cu cu ij matrix and its coefe cients eqs 15 and 16 cv cv ij matrix and its coefe cients eqs 12 and 13 c chord length ci blending function in interaction model fc polynomial function interaction model

extra heads and invariant allocations let n be an ergodic simple point process on e d and let n be its palm version thorisson ann probab 24 1996 2057 2064 proved that there exists a shift coupling of and n that is one can select a random point y of n such that translating n by y yields a configuration whose law is that of we construct shift couplings in which y and are functions of and prove that there is no shift coupling in which n is a function of the key ingredient is a deterministic translation invariant rule to allocate sets of equal volume forming a partition of r d to the points of n the construction is based on the gale shapley stable marriage algorithm amer math monthly 69 1962 9 15 next let be an ergodic random element of 0 1 zd and let be r conditioned on r 0 1 a shift coupling x of r and is called an extra head scheme we show that there exists an extra head scheme which is a function of r if and only if the marginal e r 0 is the reciprocal of an integer when the law of is product measure and d 3 we prove that there exists an extra head scheme x satisfying e exp c x d this answers a question of holroyd and liggett ann probab 29 2001 1405 1425

fractal boundaries of basin of attraction of newton raphson method in helicopter trim a key problem in helicopter aeroelastic analysis is the enormous computational time required for a numerical solution of the nonlinear system of algebraic equations required for trim particularly when free wake models are used trim requires calculation of the main rotor and tail rotor controls and the vehicle attitude which leads to the six steady forces and moments about the helicopter center of gravity to be zero an appropriate initial estimate of the trim state is needed for successful helicopter trim this study aims to determine the control inputs that can have considerable effect on the convergence of trim solution in the aeroelastic analysis of helicopter rotors by investigating the basin of attraction of the nonlinear equations set of initial guess points from which the nonlinear equations converge it is illustrated that the three main rotor pitch controls of collective pitch longitudinal cyclic pitch and lateral cyclic pitch have a significant contribution to the convergence of the trim solution trajectories of the newton iterates are shown and some ideas for accelerating the convergence of a trim solution in the aeroelastic analysis of helicopters are proposed it is found that the basins of attraction can have fractal boundaries

optimal transport and skorokhod embedding the skorokhod embedding problem is to represent a given probability as the distribution of brownian motion at a chosen stopping time over the last 50 years this has become one of the important classical problems in probability theory and a number of authors have constructed solutions with particular optimality properties these constructions employ a variety of techniques ranging from excursion theory to potential and pde theory and have been used in many different branches of pure and applied probability we develop a new approach to skorokhod embedding based on ideas and concepts from optimal mass transport in analogy to the celebrated article of gangbo and mccann on the geometry of optimal transport we establish a geometric characterization of skorokhod embeddings with desired optimality properties this leads to a systematic method to construct optimal embeddings it allows us for the first time to derive all known optimal skorokhod embeddings as special cases of one unified construction and leads to a variety of new embeddings while previous constructions typically used particular properties of brownian motion our approach applies to all sufficiently regular markov processes

comparison of temporal and spatial direct numerical simulation of compressible boundary layer transition two models are used in the direct numerical simulation of transitional boundary layer flows the spatial model and the temporal model the spatial approach is the closest realization of a transition experiment but is significantly more expensive than the temporal approach which employs a local parallel flow assumption in its formulation because of the parallel flow assumption a temporal approach cannot take into account the nonparallel effects of boundary layer flows properly the consequence of this defect has never been addressed adequately in this study the results from various temporal approaches are compared extensively to those obtained by our two newly developed spatial direct numerical simulation codes for nonlinear subharmonic transition and oblique wave breakdown at mach numbers 1 6 and 4 5 a recently developed new temporal approach that can include some nonparallel effects in the computation is also introduced the use of our new formulation is essential in obtaining quantitative agreement with the spatial approach at high mach numbers whereas the standard temporal approach does not give satisfactory results

outflow boundary conditions for spatial navier stokes simulations of transition boundary layers for numerical simulations of the spatially evolving laminar turbulent transition process in boundary layers using the complete navier stokes equations the treatment of the outflow boundary requires special attention the disturbances must pass through this boundary without causing reflections that would significantly alter the flow upstream in this paper we present various methods to influence the disturbed flow downstream of the region of interest such that the disturbance level at the outflow boundary is significantly reduced and hence the possibility of reflections is minimized to demonstrate the effectiveness of the various techniques to alter the disturbance flow near the outflow boundary the fundamental breakdown of a strongly decelerated boundary layer is simulated our results show that the most effective method is to spatially suppress the disturbance vorticity within a so called relaminarization zone the suppression of the disturbance vorticity is gradually imposed within this zone by means of a weighting function the enforced decay of the disturbance vorticity leads to a practically complete dissipation of any fluctuating component most importantly this technique causes only a negligible upstream effect the relaminarized boundary layer flow then passes through the outflow boundary without significant reflections

spatial three dimensional secondary instability of compressible boundary layer flows three dimensional linear secondary instability theory is extended for compressible and high mach number boundary layer flows the effect of a small but finite amplitude compressible tollmien schlichting wave on the growth of dimensional perturbations is investigated the focus is on principal parametric resonance responsible for the strong growth of subharmonics in a low disturbance environnement the effect of increasing number on the onset growth and shape of eigenfunctions of the subharmonics is assessed and the resulting vortical structure is examined

verification and validation of a direct numerical simulation code abstract the verification of a direct numerical simulation code is carried out using the method of manufactured solutions numerical results from the code are also compared with experimental and linear stability theory results in a boundary layer over an airfoil displacement thickness momentum thickness and shape factor are used to measure the boundary layer comparisons considering the amplitude of the velocity disturbance caused by two dimensional tollmien schlichting waves are also made the results show the verification and validation of the direct numerical simulation code

moderate deviations for empirical measures of markov chains lower bounds we obtain upper bounds for moderate deviations of empirical measures of markov chains with general state space in the topology under the minimal assumption of geometric ergodicity the regeneration split chain method and a result on projective systems are employed in the proof

the range of stable random walks limit theorems are proved for the range of d dimensional random walks in the domain of attraction of a stable process of index p3 the range rn is the number of distinct sites of zd visited by the random walk before time n our results depend on the value of the ratio 3 d the most interesting results are obtained for 2 3 1 which can only occur if d 1 we prove the convergence in distribution of rn e rn toward some constant times the lebesgue measure of the range of the limiting stable process some of our results require regularity assumptions on the characteristic function of x

infinite clusters in dependent automorphism invariant percolation on trees we study dependent bond percolation on the homogeneous tree t n of order n 2 under the assumption of automorphism invariance excluding a trivial case we find that the number of infinite clusters a s is either 0 or furthermore each infinite cluster a s has either 1 2 or infinitely many topological ends and infinite clusters with infinitely many topological ends have a s a branching number greater than 1 we also show that if the marginal probability that a single edge is open is at least 2 n 1 then the existence of infinite clusters has to have positive probability several concrete examples are considered

functional central limit theorem for a class of negatively dependent heavy tailed stationary infinitely divisible processes generated by conservative flows we prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes the limiting stable process is particularly interesting due to its long memory which is quantified by a mittag leffler process induced by an associated harris chain at the discrete time level previous results in owada and samorodnitsky ann probab 43 2015 240 285 dealt with positive dependence in the increment process whereas this paper derives the functional limit theorems under negative dependence the negative dependence is due to cancellations arising from gaussian type fluctuations of functionals of the associated harris chain the new types of limiting processes involve stable random measures due to heavy tails mittag leffler processes due to long memory and brownian motions due to the gaussian second order cancellations along the way we prove a function central limit theorem for fluctuations of functionals of harris chains which is of independent interest as it extends a result of chen probab theory related fields 116 2000 89 123

gravitational allocation to poisson points for d 3 we construct a non randomized fair and translationequivariant allocation of lebesgue measure to the points of a standard poisson point process in r d defined by allocating to each of the poisson points its basin of attraction with respect to the flow induced by a gravitational force field exerted by the points of the poisson process we prove that this allocation rule is economical in the sense that the allocation diameter defined as the diameter x of the basin of attraction containing the origin is a random variable with a rapidly decaying tail specifically we have the tail bound p x r c exp h cr logr d i

self similar random measures a set is called self similar if it is decomposable into parts which are similar to the whole this notion was generalized to random sets in the present paper an alternative axiomatic approach is given which makes precise the following idea using palm distribution theory a random set is statistically self similar if it is statistically scale invariant with respect to any center chosen at random from that set for these sets hausdorff dimension coincides with an intrinsic self similarity index

a new time space domain high order finite difference method for the acoustic wave equation a new unified methodology was proposed in finkelstein and kastner 2007 39 to derive spatial finite difference fd coefficients in the joint time space domain to reduce numerical dispersion the key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies we develop this new time space domain fd method further for 1d 2d and 3d acoustic wave modeling using a plane wave theory and the taylor series expansion new spatial fd coefficients are frequency independent though they lead to a frequency dependent numerical solution we prove that the modeling accuracy is 2nd order when the conventional 2m th order space domain fd and the 2nd order time domain fd stencils are directly used to solve the acoustic wave equation however under the same discretization the new 1d method can reach 2m th order accuracy and is always stable the 2d method can reach 2m th order accuracy along eight directions and has better stability similarly the 3d method can reach 2m th order accuracy along 48 directions and also has better stability than the conventional fd method the advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models in addition we study the influence of the fd stencil length on numerical modeling for 1d inhomogeneous media and derive an optimal fd stencil length required to balance the accuracy and efficiency of modeling a new time space domain high order staggered grid fd method for the 1d acoustic wave equation with variable densities is also developed which has similar advantages demonstrated by dispersion analysis stability analysis and modeling experiments the methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering

invariant transports of stationary random measures and mass stationarity we introduce and discuss balancing invariant transports of stationary random measures on a polish abelian group the first main result is an associated fundamental invariance property of palm measures derived from a generalization of neveu s exchange formula the second main result is a simple sufficient and necessary criterion for the existence of balancing invariant transports we then introduce in a non stationary setting the concept of mass stationarity with respect to a random measure formalizing the intuitive idea that the origin is a typical location in the mass the third main result of the paper is that a measure is a palm measure if and only if it is mass stationary

freestream capturing for moving coordinates in three dimensions a detailed formula is developed that can be used in both finite volume fv and finite difference fd methods for constructing freestream capturing metrics in space and time it is shown that considering an fv cell on the fd grid the freestream capturing metrics in space and time can be constructed from the fd formulation the approach is costly but guarantees the global conservation for an arbitrary motion of the grid

homogenization of dirichlet parabolic problems for coefficients and open sets simultaneously variable and applications to optimal design in a previous paper we studied the homogenization of a sequence of parabolic linear dirichlet problems when the coefficients and the domains vary arbitrarily here we improve the convergence result given in this paper by showing the strong convergence in l2 every time this is applied to obtain an existence result for control problems in optimal design written in a relaxed form the control variables are the material and the shape

poisson splitting by factors given a homogeneous poisson process on d with intensity we prove that it is possible to partition the points into two sets as a deterministic function of the process and in an isometry equivariant way so that each set of points forms a homogeneous poisson process with any given pair of intensities summing to in particular this answers a question of ball electron commun probab 10 2005 60 69 who proved that in d 1 the poisson points may be similarly partitioned via a translation equivariant function so that one set forms a poisson process of lower intensity and asked whether the same is possible for all d we do not know whether it is possible similarly to add points again chosen as a deterministic function of a poisson process to obtain a poisson process of higher intensity but we prove that this is not possible under an additional finitariness condition

a compact difference scheme for the navier stokes equations in vorticity velocity formulation this paper presents a new numerical method for solving the incompressible unsteady navier stokes equations in vorticity velocity formulation the method is applicable to spatial simulations of transitional and turbulent boundary layer flows it is based on a compact difference discretization of the streamwise and wall normal derivatives in cartesian coordinates a fourier collocation approach is used for the spanwise derivatives important new features of the numerical method are the use of nonequidistant differences in the wall normal direction the use of split compact differences in the streamwise direction a new fast iteration for a semi implicit time integration of the wall normal diffusion terms and an improvement of the buffer domain technique to prevent reflections of waves at the outflow boundary results of test calculations are presented to verify the improvements obtained by the use of these new techniques

skorokhod embeddings minimality and non centred target distributions in this paper we consider the skorokhod embedding problem for target distributions with non zero mean in the zero mean case uniform integrability provides a natural restriction on the class of embeddings but this is no longer suitable when the target distribution is not centred instead we restrict our class of stopping times to those which are minimal and we find conditions on the stopping times which are equivalent to minimality

a lagged implicit segregated data reconstruction procedure to treat open boundaries the problem of treating open boundaries is still a challenging one applying fully developed condition is constrained to long enough domains without having enough physical evidence about what happens on boundaries the domain extent could not be shortened and computational costs could not be reduced from the advent of free open boundary conditions they were confined to mixed finite element procedures recent works have extended their application to coupled finite volume solvers based on the shape function data reconstruction a wider class of flow solvers available however rely on the segregated procedure where the velocity components and pressure are solved in succession moreover many finite volume algorithms do not use the shape function reconstruction in this work by proposing a lagged implicit procedure we have extended the application of the open boundary condition to these wider classes of flow solvers the proposed extension is a combination of lagged implicit data reconstruction and overall mass conservation enforcement which is easily applicable to any segregated and coupled flow solver to validate the compatibility of this extension benchmark problem of backward facing step is solved on successively truncated domains where open boundary may pass through recirculation zones results show that the proposed extension works fine for that problem it reduced the computational domain length and hence memory by a factor of 4 6 and the required computational time by a factor of 21 flow passing a cylinder is also solved which proves that the method could be applied to external flow problems as well

unbiased shifts of brownian motion let b b t t r be a two sided standard brownian motion an unbiased shift of b is a random time t which is a measurable function of b such that b t t b t t r is a brownian motion independent of b t we characterise unbiased shifts in terms of allocation rules balancing mixtures of local times of b for any probability distribution on r we construct a stopping time t 0 with the above properties such that b t has distribution we also study moment and minimality properties of unbiased shifts a crucial ingredient of our approach is a new theorem on the existence of allocation rules balancing stationary diffuse random measures on r another new result is an analogue for diffuse random measures on r of the cycle stationarity characterisation of palm versions of stationary simple point processes

efficient algorithm on a nonstaggered mesh for simulating rayleigh benard convection in a box an efficient semi implicit second order accurate finite difference method is described for studying incompressible rayleigh benard convection in a box with sidewalls that are periodic thermally insulated or thermally conducting operator splitting and a projection method reduce the algorithm at each time step to the solution of four helmholtz equations and one poisson equation and these are are solved by fast direct methods the method is numeri cally stable even though all field values are placed on a single non staggered mesh commensurate with the boundaries the efficiency and accuracy of the method are characterized for several representative convection problems

asymptotic behaviour of linear dirichlet parabolic problems with variable operators depending on time in varying domains abstract we study the asymptotic behaviour of the solutions of linear parabolic dirichlet problems when the coefficients and the domains where the problems are posed vary simultaneously in the limit problem it appear the h limit of the operators and as it is usual in the homogenization of dirichlet problems a new term of order zero we also obtain a corrector result

how to find an extra head optimal random shifts of bernoulli and poisson random fields we consider the following problem given an i i d family of bernoulli random variables indexed by z d find a random occupied site x z d such that relative to x the other random variables are still i i d bernoulli results of thorisson imply that such an x exists for all d liggett proved that for d 1 there exists an x with tails p x t of order ct 1 2 but none with finite 1 2th moment we prove that for general d there exists a solution with tails of order ct d 2 while for d 2 there is none with finite first moment we also prove analogous results for a continuum version of the same problem finally we prove a result which strongly suggests that the tail behavior mentioned above is the best possible for all d

a stable marriage of poisson and lebesgue let e be a discrete set in r d call the elements of e centers the well known voronoi tessellation partitions r d into polyhedral regions of varying sizes by allocating each site of r d to the closest center here we study fair allocations of r d to e in which the regions allocated to different centers have equal volumes we prove that if e is obtained from a translation invariant point process then there is a unique fair allocation which is stable in the sense of the galeshapley marriage problem i e sites and centers both prefer to be allocated as close as possible and an allocation is said to be unstable if some site and center both prefer each other over their current allocations we show that the region allocated to each center is a union of finitely many bounded connected sets however in the case of a poisson process an infinite volume of sites are allocated to centers further away than we prove power law lower bounds on the allocation distance of a typical site it is an open problem to prove any upper bound in d 1

high order finite difference and multigrid methods for spatially evolving instability in a planar channel a computational study of the spatial instability of planar poiseuille flow is presented a fourth order finite difference with a fully implicit time marching scheme is developed on a staggered grid a semi coarsening multigrid method is applied to accelerate convergence for the implicit scheme at each time step and a line distributive relaxation is developed as a fast solver which is very robust and efficient for anisotropic grids a new treatment for outflow boundary conditions makes the buffer area as short as one wavelength the computational results demonstrate high accuracy in terms of agreement with linear theory and excellent efficiency in the sense that cost is comparable to and usually less than explicit schemes

gravitational allocation on the sphere given a collection l of n points on a sphere s n 2 of surface area n a fair allocation is a partition of the sphere into n parts each of area 1 and each is associated with a distinct point of l we show that if the n points are chosen uniformly at random and if the partition is defined by a certain gravitational potential then the expected distance between a point on the sphere and the associated point of l is o log n we use our result to define a matching between two collections of n independent and uniform points on the sphere and prove that the expected distance between a pair of matched points is o log n which is optimal by a result of ajtai komlos and tusnady

a new high order method for the simulation of incompressible wall bounded turbulent flows a new method to perform direct numerical simulations of wall bounded flows has been developed and implemented the method uses high order compact finite differences in wall normal for channel flow or radial direction for pipe flow on a collocated grid which gives high accuracy results without the effectfof filtering caused by frequent interpolation as required on a staggered grid the use of compact finite differences means that extreme clustering near the wall leading to small time steps in high reynolds number simulations is avoided the influence matrix method is used to ensure a completely divergence freesolution and all systems of equations are solved in banded form which ensures an effcient solution procedure with low requirements for data storage the method is unique in the sense that exactly divergence free solutions on collocated meshes are calculated using arbitrary dffierence matrices the code is validated for two flow cases i e turbulent channel and turbulent pipe flow at relatively low reynolds number all tests show excellent agreement with analytical and existing results confirming the accuracy and robustness ofthe method the next step is to eciently parallelise the code so that high reynolds number simulations at high resolution can be performed we furthermore investigated rare events occurring in the near wall region of turbulent wall bounded flows we find that negative streamwise velocities and extreme wall normal velocity uctuations are found rarely on the order of 0 01 and that they occur more frequently at higher reynolds number these events are caused by strong vortices lying further away from the wall and it appears that these events are universal for wall bounded flows

numerical investigation of the three dimensional development in boundary layer transition a numerical method for solving the complete navier stokes equations for incompressible flows is introduced that is applicable for investigating three dimensional transition phenomena in a spatially growing boundary layer results are discussed for a test case with small three dimensional disturbances for which detailed comparison to linear stability theory is possible the validity of our numerical model for investigating nonlinear transition phenomena is demonstrated by realistic spatial simulations of the experiments by kachanov and levchenko1 for a subharmonic resonance breakdown and of the experiments of klebanoff et al 2 for a fundamental resonance breakdown

central limit theorems for stochastic processes under random entropy conditions necessary and sufficient conditions are found for the weak convergence of the row sums of an infinitesimal row independent triangular array nj of stochastic processes indexed by a set s to a sample continuous gaussian process when the array satisfies a random entropy condition analogous to one used by gine and zinn 1984 for empirical processes this entropy condition is satisfied when s is a class of sets or functions with the vapnik ervonenkis property and each nj f fd nj is of the form njc for some reasonable random finite signed measure vnj as a result we obtain necessary and sufficient conditions for the weak convergence of possibly non i i d partial sum processes and new sufficient conditions for empirical processes indexed by vapnik ervonenkis classes special cases include prokhorov s 1956 central limit theorem for empirical processes and shorack s 1979 theorems on weighted empirical processes

characterization of palm measures via bijective point shifts the paper considers a stationary point process n in r d a point map picks a point of n in a measurable way it is called bijective thorisson h 2000 coupling stationarity and regeneration springer new york if it is generating by suitable shifts a bijective mapping on n mecke math nachr 65 1975 335 344 proved that the palm measure of n is point stationary in the sense that it is invariant under bijective point shifts our main result identifies this property as being characteristic for palm measures this generalizes a fundamental classical result for point processes on the line see e g theorem 11 4 in kallenberg o 2002 foundations of modern probability 2nd ed springer new york and solves a problem posed in thorisson h 2000 coupling stationarity and regeneration springer new york and ferrari p a landim c and thorisson h 2004 ann inst h poincare probab statist 40 141 152 our second result guarantees the existence of bijective point maps that have almost surely with respect to the palm measure of n no fixed points this answers another question asked by thorisson our final result shows that there is a directed graph with vertex set n that is defined in a translation invariant way and whose components are almost surely doubly infinite paths this generalizes and complements one of the main results in holroyd a e and peres y 2003 electron comm prohab 8 17 27 no additional assumptions as ergodicity nonlattice type conditions or a finite intensity are made in this paper

optimal transport from lebesgue to poisson this paper is devoted to the study of couplings of the lebesgue measure and the poisson point process we prove existence and uniqueness of an optimal coupling whenever the asymptotic mean transportation cost is finite moreover we give precise conditions for the latter which demonstrate a sharp threshold at d 2 the cost will be defined in terms of an arbitrary increasing function of the distance the coupling will be realized by means of a transport map allocation map which assigns to each poisson point a set cell of lebesgue measure 1 in the case of quadratic costs all these cells will be convex polytopes

how often does a harris recurrent markov chain recur let x n n geq 0 be a harris recurrent markov chain with state space e mathscr e transition probability p x a and invariant measure pi given a nonnegative pi integrable function f on e the exact asymptotic order is given for the additive functionals sum k 1 n f x k quad n 1 2 dotsin the forms of both weak and strong convergences in particular the frequency of x n n geq 0 visiting a given set a in mathscr e with 0 pi a infty is determined by taking f i a under the regularity assumption the limits in our theorems are identified the one and two dimensional random walks are taken as the examples of applications

use of finite volume schemes for transition simulation the use of finite volume methods in the study of spatially and temporally evolving transitional flows over a flat plate is investigated schemes are developed with both central and upwind differencing the compressible navier stokes equations are solved with a runge kutta time stepping scheme disturbances are determined using linear theory and superimposed at the inflow boundary time accurate integration is then used to allow temporal and spatial disturbance evolution characteristic based boundary conditions are employed the requirements of using finite volume algorithms are studied in detail special emphasis is placed on difference schemes grid resolution and disturbance amplitudes moreover comparisons are made with linear theory for small amplitude disturbances both subsonic and supersonic flows are considered and it is shown that the locations of branch 1 and branch 2 of the neutral stability curve are well predicted given sufficient resolution

on maximal hard core thinnings of stationary particle processes the present paper studies existence and distributional uniqueness of subclasses of stationary hard core particle systems arising as thinnings of stationary particle processes these subclasses are defined by natural maximality criteria we investigate two specific criteria one related to the intensity of the hard core particle process the other one being a local optimality criterion on the level of realizations in fact the criteria are equivalent under suitable moment conditions we show that stationary hard core thinnings satisfying such criteria exist and are frequently distributionally unique more precisely distributional uniqueness holds in subcritical and barely supercritical regimes of continuum percolation additionally based on the analysis of a specific example we argue that fluctuations in grain sizes can play an important role for establishing distributional uniqueness at high intensities finally we provide a family of algorithmically constructible approximations whose volume fractions are arbitrarily close to the maximum

a novel velocity vorticity formulation of the navier stokes equations with applications to boundary layer disturbance evolution a novel velocity vorticity formulation of the unsteady three dimensional navier stokes equations is presented the formulation is particularly suitable for simulating the evolution of three dimensional disturbances in boundary layers a key advantage is that there are only three governing equations for three primary dependent variables another advantage is that no wall boundary conditions are needed for the vorticity instead the conditions placed on the velocity are linked to the vorticity field through integral constraints based on the definition of vorticity numerical methods are presented in the context of application to the three dimensional boundary layer over a rotating disc the discretization scheme uses spectral expansions in the wall normal and azimuthal or spanwise directions and compact finite differences in the radial or streamwise direction the scheme is implemented so that the advantages of spectral convergence can be combined with the use of an efficient line iteration solution procedure the linearized form of the new velocity vorticity method is validated for the case of convective instabilities evolving over both rigid and compliant discs

homogenization of dirichlet parabolic systems with variable monotone operators in general perforated domains we consider the homogenization of parabolic systems with dirichlet boundary conditions when the operators and the domains in which the problems are posed vary simultaneously we assume the operators do not depend on t then we show that the corrector obtained in a previous paper for the elliptic problem still gives a corrector for the parabolic one from this result we easily obtain the limit problem in the parabolic case

estimation in nonlinear regression with harris recurrent markov chains in this paper we study parametric nonlinear regression under the harris recurrent markov chain framework we first consider the nonlinear least squares estimators of the parameters in the homoskedastic case and establish asymptotic theory for the proposed estimators our results show that the convergence rates for the estimators rely not only on the properties of the nonlinear regression function but also on the number of regenerations for the harris recurrent markov chain furthermore we discuss the estimation of the parameter vector in a conditional volatility function and apply our results to the nonlinear regression with i 1 processes and derive an asymptotic distribution theory which is comparable to that obtained by park and phillips 2001 some numerical studies including simulation and empirical application are provided to examine the finite sample performance of the proposed approaches and results

numerical experiments in boundary layer stability numerical solution of the three dimensional incompressible navier stokes equations is used to study the instability of a flat plate boundary layer in a manner analogous to the vibrating ribbon experiments flow field structures are observed which are very similar to those found in the vibrating ribbon experiment to which computational initial conditions have been matched stream wise periodicity is assumed in the simulation so that the evolution occurs in time but the events that constitute the instability are so similar to the spatially occurring ones of the laboratory that it seems clear the physical processes involved are the same a spectral and finite difference numerical algorithm is employed in the simulation

on the limit laws of the second order for additive functionals of harris recurrent markov chains let xn n 0 be a harris recurrent markov chain with state space e and invariant measure the law of the iterated logarithm and the law of weak convergence are given for the additive functionals of the form

palm pairs and the general mass transport principle we consider a lcsc group g acting on a borel space s and on an underlying finite measure space our first main result is a transport formula connecting the palm pairs of jointly stationary random measures on s a key and new technical result is a measurable disintegration of the haar measure on g along the orbits the second main result is an intrinsic characterization of the palm pairs of a g invariant random measure we then proceed with deriving a general version of the mass transport principle for possibly non transitive and non unimodular group operations first in a deterministic and then in its full probabilistic form