conditional wegner estimate for the standard random breather potential we prove a conditional wegner estimate for schrodinger operators with random potentials of breather type more precisely we reduce the proof of the wegner estimate to a scale free unique continuation principle the relevance of such unique continuation principles has been emphasized in previous papers in particular in recent years we consider the standard breather model meaning that the single site potential is the characteristic function of a ball or a cube while our methods work for a substantially larger class of random breather potentials we discuss in this particular paper only the standard model in order to make the arguments and ideas easily accessible

localization for the anderson model on a strip with singular potentials abstract we prove exponential localization in the anderson model on a one dimensional strip for any potential whose probability distribution is not concentrated on a single point and possesses some finite moment in particular we obtain localization for bernoulli potentials on a strip

localization phenomenon in gaps of the spectrum of random lattice operators we consider a class of random lattice operators including schrodinger operators of the formh w gv wherew x is a real valued periodic function g is a positive constant andv x x d are independent identically distributed real random variables we prove that if the operator w has gaps in the spectrum andg is sufficiently small then the operatorh develops pure point spectrum with exponentially decaying eigenfunctions in a vicinity of the gaps

on the lipschitz continuity of the integrated density of states for sign indefinite potentials the present paper is devoted to the study of spectral properties of random schrodinger operators using a finite section method for toeplitz matrices we prove a wegner estimate for some alloy type models where the single site potential is allowed to change sign the results apply to the corresponding discrete model too in certain disorder regimes we are able to prove the lipschitz continuity of the integrated density of states and or localization near spectral edges

microlocalization percolation and anderson localization for the magnetic schrodinger operator with a random potential abstract we study the spectral properties of the magnetic schrodinger operator with a random potential using results from microlocal analysis and percolation we show that away from the landau levels the spectrum is almost surely pure point with at least exponentially decaying eigenfunctions moreover it is shown that the rate of decay is proportional to b

non monotonic random schrodinger operators the anderson model abstract we prove exponential localization at all energies for one dimensional continuous anderson type models with single site potentials of changing sign a periodic background potential is allowed the main problem arises from non monotonicity i e the operator does not depend monotonically in the form sense on the random parameters we show that the method of two parameter spectral averaging recently devised by buschmann and stolz to prove localization for poisson and random displacement models can be modified to work for the type of anderson model considered here

optimal estimation theory for dynamic systems with set membership uncertainty an overview in many problems such as linear and nonlinear regressions parameter and state estimation of dynamic systems state space and time series prediction interpolation smoothing and functions approximation one has to evaluate some unknown variable using available data the data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables typically the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory an interesting alternative approach referred to as set membership or unknown but bounded ubb error description has been investigated since the late 1960s in this approach uncertainty is described by an additive noise which is known only to have given integral typically l2 of l1 or componentwise l bounds in this paper we review the main results of this theory with special attention to the most recent advances obtained in the case of componentwise bounds

a new proof of localization in the anderson tight binding model we give a new proof of exponential localization in the anderson tight binding model which uses many ideas of the frohlich martinelli scoppola and spencer proof but is technically simpler particularly the probabilistic estimates

on subordinacy and analysis of the spectrum of schrodinger operators with two singular endpoints the theory of subordinacy is extended to all one dimensional schrodinger operatorsfor which the corresponding differential expression l d 2 dr 2 v r is in the limit point case at both ends of an interval a b with v r locally integrable this enables a detailed classification of the absolutely continuous and singular spectra to be established in terms of the relative asymptotic behaviour of solutions of lu xu x e as r a and r b the result provides a rigorous but straightforward method of direct spectral analysis which has very general application and somefurther properties of the spectrum are deduced from the underlying theory

paradigms and puzzles in the theory of dynamical systems a self contained exposition is given of an approach to mathematical models in particular to the theory of dynamical systems the basic ingredients form a triptych with the behavior of a system in the center and behavioral equations with latent variables as side panels the author discusses a variety of representation and parametrization problems in particular questions related to input output and state models the proposed concept of a dynamical system leads to a new view of the notions of controllability and observability and of the interconnection of systems in particular to what constitutes a feedback control law the final issue addressed is that of system identification it is argued that exact system identification leads to the question of computing the most powerful unfalsified model

localization and universality of poisson statistics for the multidimensional anderson model at weak disorder we prove anderson localization with the mean field lyapunov exponent and poisson statistics for eigenvalue spacing for the multi dimensional anderson model at weak disorder these results are obtained by developing the supersymmetric formalism initiated in w1 see also sjw rid

an extension of kotani s theorem to random generalized sturm liouville operators we consider the random operator d m dx d dx q x wherem dx andq x are a stationary ergodic random measure and a random function respectively to this general case we extend kotani s theorem which asserts that the absolutely continuous spectrum is completely determined by the ljapounov indices our framework includes the case of stochastic jacobi matrices treated by simon

worst case system identification in l 1 ne equation 1 optimal algorithms and error bounds abstract this paper analyses worst case identification of linear shift invariant systems with an l 1 error criterion the assumed apriori information on the plant are bounds on the system gain and decay rate of the impulse response of the unknown system and the experimental data is assumed to be a finite set of corrupted impulse or step response samples of the system

extended states in the anderson model on the bethe lattice abstract we prove that the anderson hamiltonianh von the bethe lattice has extended states for small disorder more precisely given any closed intervalicontained in the interior of the spectrum of the laplacian on the bethe lattice we prove that for small disorderh has purely absolutely continuous spectrum iniwith probability one i e ac h i iand pp h i sc h i with probability one and its integrated density of states is continuously differentiable on the intervali

identification and application of bounded parameter models abstract the place of parameter bounding algorithms in identification methodology is discussed such algorithms provide a radical alternative to the computation of parameter point estimates and covariances instead of p d f or mean and covariance for the noise and prior parameter estimates they require bounds in an essentially deterministic model formulation the paper is a preliminary review of some standard tasks namely experiment design testing for outliers toleranced prediction and worst case control design in the context of parameter bounding identification computational requirements of these tasks are examined and the limitations of existing parameter bounding algorithms are noted

landau hamiltonians with random potentials localization and the density of states we prove the existence of localized states at the edges of the bands for the two dimensional landau hamiltonian with a random potential of arbitrary disorder provided that the magnetic field is sufficiently large the corresponding eigenfunctions decay exponentially with the magnetic field and distance we also prove that the integrated density of states is lipschitz continuous away from the landau energies the proof relies on a wegner estimate for the finite area magnetic hamiltonians with random potentials and exponential decay estimates for the finitearea green s functions the proof of the decay estimates for the green s functions uses fundamental results from two dimensional bond percolation theory

low lying eigenvalues of randomly curved quantum waveguides abstract we consider the negative dirichlet laplacian on an infinite waveguide embedded in r 2 and finite segments thereof the waveguide is a perturbation of a periodic strip in terms of a sequence of independent identically distributed random variables which influence the curvature we derive explicit lower bounds on the first eigenvalue of finite segments of the randomly curved waveguide in the small coupling i e weak disorder regime this allows us to estimate the probability of low lying eigenvalues a tool which is relevant in the context of anderson localization for random schrodinger operators

generalized eigenfunctions for waves in inhomogeneous media abstract many wave propagation phenomena in classical physics are governed by equations that can be recast in schrodinger form in this approach the classical wave equation e g maxwell s equations acoustic equation elastic equation is rewritten in schrodinger form leading to the study of the spectral theory of its classical wave operator a self adjoint partial differential operator on a hilbert space of vector valued square integrable functions physically interesting inhomogeneous media give rise to nonsmooth coefficients we construct a generalized eigenfunction expansion for classical wave operators with nonsmooth coefficients our construction yields polynomially bounded generalized eigenfunctions the set of generalized eigenvalues forming a subset of the operator s spectrum with full spectral measure

on continuity and consistency of l optimal models this paper is concerned with the question of continuity of the mapping from observed time series to models the behavioral framework is adopted to formalize a model identification problem in which the observed time series is decomposed into a part explained by a model and a remaining part which is ascribed to noise the misfit between data and model is defined symmetrically in the system variables and measured in the l or amplitude norm with the introduction of proper notions of convergence it is shown that the misfit function continuously depends on both the data and the model two notions of consistency are formalized and it is shown that the continuity of the misfit function implies a consistent identification of optimal and suboptimal models

localization in general one dimensional random systems i jacobi matrices we consider random discrete schrodinger operators in a strip with a potentialv n n a label in and a finite label across the strip andv an ergodic process we prove thath0 v has only point spectrum with probability one under two assumptions 1 theconditional distribution of v n n 0 1 all conditioned on v n 0 1 all has an absolutely continuous component with positive probability 2 for a e e no lyaponov exponent is zero

localization for random and quasiperiodic potentials a survey is made of some recent mathematical results and techniques for schrodinger operators with random and quasiperiodic potentials a new proof of localization for random potentials established in collaboration with h von dreifus is sketched

dynamical localization for discrete and continuous random schrodinger operators we show for a large class of random schrodinger operators h on and on that dynamical localization holds i e that with probability one for a suitable energy interval i and for q a positive real here is a function of sufficiently rapid decrease and p i h is the spectral projector of h corresponding to the interval i the result is obtained through the control of the decay of the eigenfunctions of h and covers in the discrete case the anderson tight binding model with bernoulli potential dimension 1 or singular potential 1 and in the continuous case anderson as well as random landau hamiltonians

delocalization in random polymer models a random polymer model is a one dimensional jacobi matrix randomly composed of two finite building blocks if the two associated transfer matrices commute the corresponding energy is called critical such critical energies appear in physical models an example being the widely studied random dimer model it is proven that the lyapunov exponent vanishes quadratically at a generic critical energy and that the density of states is positive there large deviation estimates around these asymptotics allow to prove optimal lower bounds on quantum transport showing that it is almost surely overdiffusive even though the models are known to have pure point spectrum with exponentially localized eigenstates for almost every configuration of the polymers furthermore the level spacing is shown to be regular at the critical energy

anderson localization for bernoulli and other singular potentials we prove exponential localization in the anderson model under very weak assumptions on the potential distribution in one dimension we allow any measure which is not concentrated on a single point and possesses some finite moment in particular this solves the longstanding problem of localization for bernoulli potentials i e potentials that take only two values in dimensions greater than one we prove localization at high disorder for potentials with holder continuous distributions and for bounded potentials whose distribution is a convex combination of a holder continuous distribution with high disorder and an arbitrary distribution these include potentials with singular distributions we also show that for certain bernoulli potentials in one dimension the integrated density of states has a nontrivial singular component

worst case identification in banach spaces a general formulation of worst case identification of linear systems in a banach space framework is discussed this enables one to prove generalizations of various existence theorems from the theory of robust l1 and h identification to a variety of other situations

localization for one dimensional continuum bernoulli anderson models we use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional continuum anderson type models with singular distributions in particular the case of a bernoulli dis tribution is covered the operators we consider model alloys composed of at least two distinct types of randomly dispersed atoms our main tools are the reflection and transmission coefficients for compactly supported single site perturbations of a periodic background which we use to verify the necessary hypotheses of multi scale analysis we show that non reflectionless single sites lead to a discrete set of exceptional energies away from which localization occurs

singular continuous spectrum under rank one perturbations and localization for random hamiltonians we consider a selfadjoint operator a and a selfadjoint rank one projection p onto a vector which is cyclic for a in terms of the spectral measure d a we give necessary and sufficient conditions for a p to have empty singular continuous spectrum or to have only point spectrum for a e we apply these results to questions of localization in the one and multi dimensional anderson models

low energy properties of the random displacement model abstract we study low energy properties of the random displacement model a random schrodinger operator describing an electron in a randomly deformed lattice all periodic displacement configurations which minimize the bottom of the spectrum are characterized while this configuration is essentially unique for dimension greater than one there are infinitely many different minimizing configurations in the one dimensional case the latter leads to unusual low energy asymptotics for the integrated density of states of the one dimensional random displacement model for symmetric bernoulli distributed displacements it has a 1 log 2 singularity at the bottom of the spectrum in particular it is not holder continuous

dynamical localization ii with an application to the almost mathieu operator several recent works have established dynamical localization for schrodinger operators starting from control on the localization length of their eigenfunctions in terms of their centers of localization we provide an alternative way to obtain dynamical localization without resorting to such a strong condition on the exponential decay of the eigenfunctions furthermore we illustrate our purpose with the almost mathieu operator h cos 2 x 15 and with good diophantine properties more precisely for almost all for all q 0 and for all functions l2 mathbb z of compact support we show that mathop sup limits t left langle e ith theta lambda omega psi left x right q e ith theta lambda omega psi right rangle c psi the proof applies equally well to discrete and continuous random hamiltonians in all cases it uses as input a repulsion principle of singular boxes supplied in the random case by the multi scale analysis

spectral averaging techniques for jacobi matrices spectral averaging techniques for one dimensional discrete schrodinger operators are revisited and extended in particular simultaneous averaging over several parameters is discussed special focus is put on proving lower bounds on the density of the averaged spectral measures these wegner type estimates are used to analyze stability properties for the spectral types of jacobi matrices under local perturbations

lower transport bounds for one dimensional continuum schrodinger operators we prove quantum dynamical lower bounds for one dimensional continuum schrodinger operators that possess critical energies for which there is slow growth of transfer matrix norms and a large class of compactly supported initial states this general result is applied to a number of models including the bernoulli anderson model with a constant single site potential

optimal asymptotic identification under bounded disturbances the intrinsic limitation of worst case identification of linear time invariant systems using data corrupted by bounded disturbances when the unknown plant is known to belong to a given model set is studied this is done by analyzing the optimal worst case asymptotic error achievable by performing experiments using any bounded input and estimating the plant using any identification algorithm it is shown that under some topological conditions on the model set there is an identification algorithm which is asymptotically optimal for any input and the optimal asymptotic error is characterized as a function of the inputs these results which hold for any error metric and disturbance norm are applied to three specific identification problems identification of stable systems in the l sub 1 norm identification of stable rational systems in the h sub infinity norm and identification of unstable rational systems in the gap metric for each of these problems the general characterization of optimal asymptotic error is used to find near optimal inputs to minimize the error

constructive proof of localization in the anderson tight binding model we prove that for large disorder or near the band tails the spectrum of the anderson tight binding hamiltonian with diagonal disorder consists exclusively of discrete eigenvalues the corresponding eigenfunctions are exponentially well localized these results hold in arbitrary dimension and with probability one in one dimension we recover the result that all states are localized for arbitrary energies and arbitrarily small disorder our techniques extend to other physical systems which exhibit localization phenomena such as infinite systems of coupled harmonic oscillators or random schrodinger operators in the continuum

optimal volume wegner estimate for random magnetic laplacians on z2 we consider a two dimensional magnetic schrodinger operator on a square lattice with a spatially stationary random magnetic field we prove a wegner estimate with optimal volume dependence the wegner estimate holds around the spectral edges and it implies holder continuity of the integrated density of states in this region the proof is based on the wegner estimate obtained in erd s and hasler wegner estimate for random magnetic laplacians on z2 ann henri poincare 12 1719 1731 2012 10 1007 s00023 012 0177 9

modeling rationality to control self organization of crowds an environmental approach in this paper we propose a classification of crowd models in built environments based on the assumed pedestrian ability to foresee the movements of other walkers at the same time we introduce a new family of macroscopic models which make it possible to tune the degree of predictiveness i e rationality of the individuals by means of these models we describe both the natural behavior of pedestrians i e their expected behavior according to their real limited predictive ability and a target behavior i e a particularly efficient behavior one would like them to assume e g for logistic or safety reasons then we tackle a challenging shape optimization problem which consists in controlling the environment in such a way that the natural behavior is as close as possible to the target one thereby inducing pedestrians to behave more rationally than they naturally would we present numerical tests which elucidate the role of rational predictive abilities and show some promising results about the

the turnpike property in finite dimensional nonlinear optimal control turnpike properties have been established long time ago in finite dimensional optimal control problems arising in econometry they refer to the fact that under quite general assumptions the optimal solutions of a given optimal control problem settled in large time consist approximately of three pieces the first and the last of which being transient short time arcs and the middle piece being a long time arc staying exponentially close to the optimal steady state solution of an associated static optimal control problem we provide in this paper a general version of a turnpike theorem valuable for nonlinear dynamics without any specific assumption and for very general terminal conditions not only the optimal trajectory is shown to remain exponentially close to a steady state but also the corresponding adjoint vector of the pontryagin maximum principle the exponential closedness is quantified with the use of appropriate normal forms of riccati equations we show then how the property on the adjoint vector can be adequately used in order to initialize successfully a numerical direct method or a shooting method in particular we provide an appropriate variant of the usual shooting method in which we initialize the adjoint vector not at the initial time but at the middle of the trajectory

brownian survival and lifshitz tail in perturbed lattice disorder abstract we consider the annealed asymptotics for the survival probability of brownian motion among randomly distributed traps the configuration of the traps is given by independent displacements of the lattice points we determine the long time asymptotics of the logarithm of the survival probability up to a multiplicative constant as applications we show the lifshitz tail effect of the density of states of the associated random schrodinger operator and derive a quantitative estimate for the strength of intermittency in the parabolic anderson problem

localization of classical waves ii electromagnetic waves we consider electromagnetic waves in a medium described by a position dependent dielectric constant we assume that is a random perturbation of a periodic function and that the periodic maxwell operator has a gap in the spectrum where we prove the existence of localized waves i e finite energy solutions of maxwell s equations with the property that almost all of the wave s energy remains in a fixed bounded region of space at all times localization of electromagnetic waves is a consequence of anderson localization for the self adjoint operators we prove that in the random medium described by the random operator exhibits anderson localization inside the gap in the spectrum of this is shown even in situations when the gap is totally filled by the spectrum of the random operator we can prescribe random environments that ensure localization in almost the whole gap

localization for random schrodinger operators with correlated potentials we prove localization at high disorder or low energy for lattice schrodinger operators with random potentials whose values at different lattice sites are correlated over large distances the class of admissible random potentials for our multiscale analysis includes potentials with a stationary gaussian distribution whose covariance functionc x y decays as x y where 0 can be arbitrarily small and potentials whose probability distribution is a completely analytical gibbs measure the result for gaussian potentials depends on a multivariable form of nelson s best possible hypercontractive estimate

the lp theory of the spectral shift function the wegner estimate and the integrated density of states for some random operators we develop the l p theory of the spectral shift function for p 1 applicable to pairs of self adjoint operators whose difference is in the trace ideal p for 0 p 1 this result is a key ingredient of a new short proof of the wegner estimate applicable to a wide variety of additive and multiplicative random perturbations of deterministic background operators the proof yields the correct volume dependence of the upper bound this implies the local holder continuity of the integrated density of states at energies in the unperturbed spectral gap under an additional condition of the single site potential local holder continuity is proved at all energies this new wegner estimate together with other standard results establishes exponential localization for a new family of models for additive and multiplicative perturbations

the spectral minimum for random displacement models consider a one dimensional schrodinger operator with potential v given as follows fix a single site potential f which is supported in an interval of length less than 1 construct v by placing a translate of f into each unit interval n n 1 for an integer n where otherwise the positions of each translate are arbitrary which configuration of single sites minimizes the spectral minimum of the schrodinger operator with potential v this question is equivalent to finding the spectral minimum of the random displacement model we conjecture that the minimum is realized through pair formation of the single sites we provide a partial proof of this conjecture and additional numerical evidence for its correctness

power law bounds on transfer matrices and quantum dynamics in one dimension we present an approach to quantum dynamical lower bounds for discrete one dimensional schrodinger operators which is based on power law bounds on transfer matrices it suffices to have such bounds for a nonempty set of energies we apply this result to various models including the fibonacci hamiltonian

optimal control models of goal oriented human locomotion in recent papers it has been suggested that human locomotion may be modeled as an inverse optimal control problem in this paradigm the trajectories are assumed to be solutions of an optimal control problem that has to be determined we discuss the modeling of both the dynamical system and the cost to be minimized and we analyze the corresponding optimal synthesis the main results describe the asymptotic behavior of the optimal trajectories as the target point goes to infinity

bounded sobolev norms for linear schrodinger equations under resonant perturbations abstract we prove that the sobolev norms for a 1 d periodic schrodinger equation remain bounded under small resonant perturbations

anderson localization for random schrodinger operators with long range interactions we prove pure point spectrum with exponentially decaying eigenfunctions at all band edges for schrodinger operators with a periodic potential plus a random potential of the form v w x q i w f x i where f decays at infinity like x m for m 4d resp m 3d depending on the regularity of f the random variables q i are supposed to be independent and identically distributed we assume that their distribution has a bounded density of compact support

localization in one dimensional random media a scattering theoretic approach we use scattering theoretic methods to prove exponential localization for random displacement models in one dimension the operators we consider model both quantum and classical wave propagation our main tools are the reflection and transmission coefficients for compactly supported single site perturbations we show that randomly displaced non reflectionless single sites lead to localization

minimizing the ground state energy of an electron in a randomly deformed lattice we provide a characterization of the spectral minimum for a random schrodinger operator of the form h delta sum i in mathbb z d q x i omega i in l 2 mathbb r d where the single site potential q is reflection symmetric compactly supported in the unit cube centered at 0 and the displacement parameters i are restricted so that adjacent single site potentials do not overlap in particular we show that a minimizing configuration of the displacements is given by a periodic pattern of densest possible 2 d clusters of single site potentials

how to prove dynamical localization let h be a self adjoint operator on l 2 z d or l 2 r d with pure point spectrum on some interval i we establish general necessary and sufficient conditions for dynamical localization for a given vector and on the interval of energies i the sufficient conditions we obtain improve the existing ones such as sule or wule and can be useful in applications

anderson localization for the almost mathieu equation iii semi uniform localization continuity of gaps and measure of the spectrum we show that the almost mathieu operator has semi uniform and thus dynamical localization for 15 and a e we also obtain a new estimate on gap continuity in for this operator with 29 or 4 29 and use it to prove that the measure of its spectrum is equal to for in this range and all irrational s

localization in general one dimensional random systems we discuss two ways of extending the recent ideas of localization from discrete schrodinger operators jacobi matrices to the continuum case one case allows us to prove localization in the goldshade molchanov pastur model for a larger class of functions than previously the other method studies the model v wherev is a random constant in each hyper cube we extend wegner s result on the lipschitz nature of the ids to this model

system identification by dynamic factor models this paper concerns the modeling of stochastic processes by means of dynamic factor models in such models the observed process is decomposed into a structured part called the latent process and a remainder that is called noise the observed variables are treated in a symmetric way so that no distinction between inputs and outputs is required this motivates the additional condition that the prior assumptions on the noise are symmetric in nature one of the central questions in this paper is how uncertainty about the noise structure translates into nonuniqueness of the possible underlying latent processes we investigate several possible noise specifications and analyze properties of the resulting class of observationally equivalent factor models this concerns in particular the characterization of optimal models and properties of continuity and consistency

localization for some continuous random hamiltonians in d dimensions abstract we prove the existence with probability one of an interval of pure point spectrum for some families of continuous random schrodinger operators in d dimensions for anderson like models with positive short range single site potentials we also prove that the corresponding eigenfunctions decay exponentially and that the integrated density of states is lipschitz continuous for the other families of random potentials that we study we show that the corresponding eigenfunctions decay faster than an inverse power of x which depends upon the decay rate of the single site potential to obtain these results we develop an extension of the classical aronszajn donoghue theory for a class of relatively compact perturbations and a spectral averaging method which extends kotani s trick to these more general families of operators

the integrated density of states for some random operators with nonsign definite potentials we study the integrated density of states of random anderson type additive and multiplicative perturbations of deterministic background operators for which the single site potential does not have a fixed sign our main result states that under a suitable assumption on the regularity of the random variables the integrated density of states of such random operators is locally holder continuous at energies below the bottom of the essential spectrum of the background operator for any nonzero disorder and at energies in the unperturbed spectral gaps provided the randomness is sufficiently small the result is based on a proof of a wegner estimate with the correct volume dependence the proof relies upon the lp theory of the spectral shift function for p 1 comm math phys 218 2001 113 130 and the vector field methods of klopp comm math phys 167 1995 553 569 we discuss the application of this result to schrodinger operators with random magnetic fields and to band edge localization

localization of classical waves i acoustic waves we consider classical acoustic waves in a medium described by a position dependent mass density x we assume that x is a reandom perturbation of a periodic function 0 x and that the periodic acoustic operator a 0 nabla cdot tfrac 1 varrho 0 x nabla has a gap in the spectrum we prove the existence of localized waves i e finite energy solutions of the acoustic equations with the property that almost all of the wave s energy remains in a fixed bounded region of space at all times with probability one localization of acoustic waves is a consequence of anderson localization for the self adjoint operators a nabla cdot tfrac 1 varrho 0 x nabla onl2 d we prove that in the random medium described by x the random operatora exhibits anderson localization inside the gap in the spectrum ofa0 this is shown even in situations when the gap is totally filled by the spectrum of the random opertor we can prescribe random environments that ensure localization in almost the whole gap

on absence of diffusion near the bottom of the spectrum for a random schrodinger operator on l 2 bf r nu we consider a random schrodinger operator onl2 v of the form h omega delta v omega v omega x sigma chi c i x q i omega ci being a covering of v with unit cubes around the sites of v and qi i i d random variables with values in 0 1 we assume that theqi s are continuously distributed with bounded densityf q and that 0 p q0 1 2 1 then we show that an ergodic mean of the quantity dx x 2 exp ith x 2 t 1 vanishes provided ge h where is well localized around the origin andge is a positivec function with support in 0 e e e f our estimate ofe f is such that the set x v v x e f may contain with probability one an infinite cluster of cubes ci which are nearest neighbours the proof is based on the technique introduced by frohlich and spencer for the analysis of the anderson model

localization for some continuous random schrodinger operators we study the spectrum of random schrodinger operators acting onl2 r d of the following type h delta w sum x in mathbb z d t x v x the t x x in mathbb z d are i i d random variables under weak assumptions onv we prove exponential localization forh at the lower edge of its spectrum in order to do this we give a new proof of the wegner estimate that works without sign assumptions onv

inverse tunnelingestimates and applications to the study of spectral statistics ofrandom operators on the real line we present a proof of a minami type estimate for one dimensional random schrodinger operators valid at all energies in the localization regime provided a wegner estimate is known to hold the minami type estimate is then applied to two models to obtain results on their spectral statistics the heuristics underlying our proof of minami type estimates is that close by eigenvalues of a one dimensional schrodinger operator correspond either to eigenfunctions that live far away from each other in space or they come from some tunneling phenomena in the second case one can undo the tunneling and thus construct quasi modes that live far away from each other in space resume nous demontrons une inegalite de type minami pour des operateurs de schrodinger aleatoires uni dimensionnel dans toute la region localisee si une estimee de wegner est connue cette estimee de type de minami est alors appliquee pour obtenir les statistiques spectrales pour deux modeles l heuristique qui guide ce travail est que des valeurs propres proches pour un operateur de schrodinger sur un intervalle sont soient localisees loin l une de l autre soit sont la consequence d un phenomene d effet tunnel dans le second cas on peut en defaisant cet effet tunnel construire des quasi modes qui sont localises loin l un de l autre 0 introduction consider the following two random operators on the real line the anderson model 0 1 h d2 dx2 w

residence time of symmetric random walkers in a strip with large reflective obstacles we study the effect of a large obstacle on the so called residence time i e the time that a particle performing a symmetric random walk in a rectangular two dimensional 2d domain needs to cross the strip we observe complex behavior we find out that the residence time does not depend monotonically on the geometric properties of the obstacle such as its width length and position in some cases due to the presence of the obstacle the mean residence time is shorter with respect to the one measured for the obstacle free strip we explain the residence time behavior by developing a one dimensional 1d analog of the 2d model where the role of the obstacle is played by two defect sites having smaller probability to be crossed with respect to all the other regular sites the 1d and 2d models behave similarly but in the 1d case we are able to compute exactly the residence time finding a perfect match with the monte carlo simulations

generic sets in spaces of measures and generic singular continuous spectrum for delone hamiltonians we show that geometric disorder leads to some purely singular continuous spectrum generically the main input is a result of simon known as the wonderland theorem in 17 section 2 here we provide an alternative approach and actually a slight strengtheningbyshowingthatvarioussetsofmeasuresdefinedbyregularityproperties aregenericinthesetofallmeasuresonalocallycompactmetricspace asabyproduct we obtain the fact that a generic measure on euclidean space is singular continuous

identification of factor models by behavioural and subspace methods the behavioural framework has several attractions to offer for the identification of multivariable systems some of the variables may be left unexplained without the need for a distinction between inputs and outputs criteria for model quality are independent of the chosen parametrization and behaviours allow for a global i e non local approximation of the system dynamics this is illustrated by the identification of dynamic factor models behavioural least squares is a natural method for this problem and a comparison is given with non behavioural methods

bootstrap multiscale analysis and localization in random media we introduce an enhanced multiscale analysis that yields subexponentially decaying probabilities for bad events for quantum and classical waves in random media we obtain exponential decay for the resolvent of the corresponding random operators in boxes of side l with probability higher than 1 e l for any 0 1 the starting hypothesis for the enhanced multiscale analysis only requires the verification of polynomial decay of the finite volume resolvent at some sufficiently large scale with probability bigger than 1 d is the dimension note that from the same starting hypothesis we get conclusions that are valid for any 0 1 this is achieved by the repeated use of a bootstrap argument as an application we use a generalized eigenfunction expansion to obtain strong dynamical localization of any order in the hilbert schmidt norm and better estimates on the behavior of the eigenfunctions

residence time estimates for asymmetric simple exclusion dynamics on strips abstract the target of our study is to approximate numerically and in some particular physically relevant cases also analytically the residence time of particles undergoing an asymmetric simple exclusion dynamics on a two dimensional vertical strip the sources of asymmetry are twofold i the choice of boundary conditions different reservoir levels and ii the strong anisotropy from a drift nonlinear in density with prescribed directionality we focus on the effect of the choice of anisotropy on residence time we analyze our results by means of two theoretical models a mean field and a one dimensional birth and death one for positive drift we find a striking agreement between monte carlo and theoretical results in the zero drift case we still find agreement as long as particles can freely escape the strip through the bottom boundary otherwise the two models give different predictions and their ability to reproduce numerical results depends on the horizontal displacement probability the topic is relevant for situations occurring in pedestrian flows or biological transport in crowded environments where lateral displacements of the particles occur predominantly affecting therefore in an essentially way the efficiency of the overall transport mechanism

two parameter spectral averaging and localization for non monotonic random schrodinger operators we prove exponential localization at all energies for two types of one dimensional random schr6dinger operators the poisson model and the random displacement model as opposed to anderson type models these operators are not monotonic in the random parameters therefore the classical one parameter version of spectral averaging as used in localization proofs for anderson models breaks down we use the new method of two parameter spectral averaging and apply it to the poisson as well as the displacement case in addition we apply results from inverse spectral theory which show that two parameter spectral averaging works for sufficiently many energies all but a discrete set to conclude localization at all energies

spectral extrema and lifshitz tails for non monotonous alloy type models in the present note we determine the ground state energy and study the existence of lifshitz tails near this energy for some non monotonous alloy type models here non monotonous means that the single site potential coming into the alloy random potential changes sign in particular the random operator is not a monotonous function of the random variables