layoffs and duration dependence in a model of turnover abstract a semi markov model of turnover resulting from optimizing behavior on the part of workers is developed duration dependence in the transition out of employment is modelled as resulting from a layoff probability which decreases with tenure some preliminary results based on dime data are presented these indicate that a declining hazard rate in the transition out of employment is a significant feature of the data

irreducible unitary representations of su 2 2 we give an explicit classification of the irreducible unitary representations of the simple lie group su 2 2

a tomography of the grem beyond the rem conjecture in a companion paper we proved that in a large class of gaussian disordered spin systems the local statistics of energy values near levels n 1 2 with 1 2 are described by a simple poisson process in this paper we address the issue as to whether this is optimal and what will happen if 1 2 we do this by analysing completely the gaussian generalised random energy models grem we show that the rem behaviour persists up to the level c n where c denotes the critical temperature we show that beyond this value the simple poisson process must be replaced by more and more complex mixed poisson point processes

specification diagnostics based on laguerre alternatives for econometric models of duration abstract score tests of the null hypothesis of exponentially distributed durations conditional on regressors against alternatives in a family of approximations to arbitrary distributions for non negative random variables are developed the test statistics take a simple easily calculated and interpreted form the alternatives considered are expansions of various orders in laguerre polynomials an economic model generating exponential unemployment duration is presented the statistics are applied in a look at unemployment durations in the denver income maintenance experiment data

pseudo gaussian and rank based optimal tests for random individual effects in large n small t panels we consider the problem of detecting unobserved heterogeneity that is the problem of testing the absence of random individual effects in an n t panel we establish a local asymptotic normality property with respect to intercept regression coefficient the scale parameter of the error and the scale parameter u of individual effects which is the parameter of interest for given scaled density f 1 of the error terms when n tends to infinity and t is fixed this result allows via the hk representation theorem for developing asymptotically optimal rank based tests for the null hypothesis u 0 absence of individual effects these tests are locally asymptotically optimal at correctly specified innovation densities f 1 but remain valid irrespective of the actual underlying density the limiting distribution of our test statistics is obtained both under the null and under sequences of contiguous alternatives a local asymptotic linearity property is established in order to control for the effect of substituting estimators for nuisance parameters the asymptotic relative efficiencies of the proposed procedures with respect to the corresponding pseudo gaussian parametric tests are derived in particular the van der waerden version of our rank based tests uniformly dominates from the point of view of pitman efficiency the classical honda test small sample performances are investigated via a monte carlo study and confirm theoretical findings

on the energy landscape of the mixed even p spin model we investigate the energy landscape of the mixed even p spin model with ising spin configurations we show that for any given energy level between zero and the maximal energy with overwhelming probability there exist exponentially many distinct spin configurations such that their energies stay near this energy level furthermore their magnetizations and overlaps are concentrated around some fixed constants in particular at the level of maximal energy we prove that the hamiltonian exhibits exponentially many orthogonal peaks this improves the results of chatterjee disorder chaos and multiple valleys in spin glasses 2009 and ding et al ann probab 43 6 3468 3493 2015 where the former established a logarithmic size of the number of the orthogonal peaks while the latter proved a polynomial size our second main result obtains disorder chaos at zero temperature and at any external field as a byproduct this implies that the fluctuation of the maximal energy is superconcentrated when the external field vanishes and obeys a gaussian limit law when the external field is present

non perturbative deformation quantization of cartan domains abstract we construct families of non commuting c algebras of quantized functions for bounded irreducible hermitian symmetric spaces for this procedure we use algebras of toeplitz operators defined with respect to a perturbation of the ordinary bergman metric we prove the deformation quantization conditions for these algebras

positive energy representations holomorphic discrete series and finite dimensional irreps let g be a semi simple non compact lie group with unitary lowest highest weight representations we consider explicitly the relation among three types of representations of g positive energy unitary lowest weight representations holomorphic discrete series representations and non unitary finite dimensional irreps we consider mainly the conformal groups soo n 2 treating in full detail the cases n 1 3 4

local energy statistics in disordered systems a proof of the local rem conjecture recently bauke and mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should in most circumstances be the same as in the random energy model here we give necessary conditions for this hypothesis to be true which we show to be satisfied in wide classes of examples short range spin glasses and mean field spin glasses of the sk type we also show that under certain conditions the conjecture holds even if energy levels that grow moderately with the volume of the system are considered

fluctuations of the free energy in the rem and the p spin sk models we consider the random fluctuations of the free energy in the p spin version of the sherrington kirkpatrick sk model in the high temperature regime using the martingale approach of comets and neveu as used in the standard sk model combined with truncation techniques inspired by a recent paper by talagrand on the p spin version we prove that the random corrections to the free energy are on a scale n p 2 2 only and after proper rescaling converge to a standard gaussian random variable this is shown to hold for all values of the inverse temperature smaller than a critical p we also show that p 2 in 2 as p additionally we study the formal p limit of these models the random energy model here we compute the precise limit theorem for the properly rescaled partition function at all temperatures for 2 in 2 fluctuations are found at an exponentially small scale with two distinct limit laws above and below a second critical value in 2 2 for up to that value the rescaled fluctuations are gaussian while below that there are non gaussian fluctuations driven by the poisson process of the extreme values of the random energies for larger than the critical 2 in 2 the fluctuations of the logarithm of the partition function are on a scale of 1 and are expressed in terms of the poisson process of extremes at the critical temperature the partition function divided by its expectation converges to 1 2

universality of the rem for dynamics of mean field spin glasses we consider a version of glauber dynamics for a p spin sherrington kirkpatrick model of a spin glass that can be seen as a time change of simple random walk on the n dimensional hypercube we show that for all p 3 and all inverse temperatures 0 there exists a constant p 0 such that for all exponential time scales exp n with p the properly rescaled clock process time change process converges to an stable subordinator where 2 1 moreover the dynamics exhibits aging at these time scales with a time time correlation function converging to the arcsine law of this stable subordinator in other words up to rescaling on these time scales that are shorter than the equilibration time of the system the dynamics of p spin models ages in the same way as the rem and by extension bouchaud s rem like trap model confirming the latter as a universal aging mechanism for a wide range of systems the sk model the case p 2 seems to belong to a different universality class

renormalisation of noncommutative ϕ 4 theory by multi scale analysis in this paper we give a much more efficient proof that the real euclidean 4 model on the four dimensional moyal plane is renormalisable to all orders we prove rigorous bounds on the propagator which complete the previous renormalisation proof based on renormalisation group equations for non local matrix models on the other hand our bounds permit a powerful multi scale analysis of the resulting ribbon graphs here the dual graphs play a particular role because the angular momentum conservation is conveniently represented in the dual picture choosing a spanning tree in the dual graph according to the scale attribution we prove that the summation over the loop angular momenta can be performed at no cost so that the power counting is reduced to the balance of the number of propagators versus the number of completely inner vertices in subgraphs of the dual graph

on a simple test for neglected heterogeneity in panel studies summary this paper deals with the performance of a simple test for the detection of unmeasured heterogeneity in regression models for panel data it is assumed that the unmeasured heterogeneity can be modeled by an individual specific random variable that does not vary over time conditionally on the individual specific effects and the regressor variables the distribution of the dependent variable is assumed to belong to a linear exponential family this class of distributions includes linear models for continuous dependent variables as well as nonlinear models for discrete outcomes the proposed test does not assume a special form of the distribution of the heterogeneity and the test statistic can be calculated with available computer programs the performance of the test is investigated in a simulation experiment

lie group convolution algebras as deformation quantizations of linear poisson structures introduction let l be a finite dimensional lie algebra over the real numbers r and let l be its dual vector space it is well known 24 that the lie algebra structure on l defines a natural poisson structure on l in fact this was already known to lie 24 and these poisson structures are exactly what are now called the linear poisson structures given a manifold m equipped with a poisson structure one can seek deformation quantizations in the direction of as first studied in 3 these are loosely speaking one parameter families h ler of deformations of the pointwise multiplication on c m or an appropriate subalgebra such that

elementary representations and intertwining operators for su 2 2 i the structure of the group su 2 2 and of its lie algebra is studied in detail the results will be applied in subsequent parts devoted to the explicit construction of elementary representations of su 2 2 induced from different parabolic subgroups and of the intertwining operators between these representations a summary of some results of parts ii and iii is given

universality and extremal aging for dynamics of spin glasses on subexponential time scales we consider random hopping time rht dynamics of the sherrington kirkpatrick sk model and p spin models of spin glasses for any of these models and for any inverse temperature 0 we prove that on time scales that are subexponential in the dimension the properly scaled clock process time change process of the dynamics converges to an extremal process moreover on these time scales the system exhibits aging like behavior which we call extremal aging in other words the dynamics of these models ages as the random energy model rem does hence by extension this confirms bouchaud s rem like trap model as a universal aging mechanism for a wide range of systems that for the first time includes the sk model 2011 wiley periodicals inc

a physicist s approach to number partitioning the statistical physics approach to the number partioning problem a classical np hard problem is both simple and rewarding very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase boundary that separates the easy to solve from the hard to solve phase of the npp as well as for the probability distributions of the optimal and sub optimal solutions in addition it can be shown that solving a number portioning problem of size n to some extent corresponds to locating the minimum in an unsorted list of o 2n numbers considering this correspondence it is not surprising that known heuristics for the partitioning problem are not signi4cantly better than simple random search

a branching random walk seen from the tip we show that all the time dependent statistical properties of the rightmost points of a branching brownian motion can be extracted from the traveling wave solutions of the fisher kpp equation the distribution of all the distances between the rightmost points has a long time limit which can be understood as the delay of the fisher kpp traveling waves when the initial condition is modified the limiting measure exhibits the surprising property of superposability the statistical properties of the distances between the rightmost points of the union of two realizations of the branching brownian motion shifted by arbitrary amounts are the same as those of a single realization we discuss the extension of our results to more general branching random walks

quantum field theory on quantized bergman domain we present an oscillator realization of discrete series representations of group su 2 2 we give formulas for the coherent state star product quantization of a bergman domain d a formulation of a regularized noncommutative scalar field on a quantized d is given

phase transition in the number partitioning problem universit at magdeburg institut fu r theoretische physik universit atsplatz 2 d 39106 magdeburg germany february 1 2008 number partitioning is an np complete problem of com binatorial optimization a statistical mechanics analysis re veals the existence of a phase transition that separates theeasy from the hard to solve instances and that re ects thepseudo polynomiality of number partitioning the phase di agram and the value of the typical ground state energy arecalculated 64 60 cn 02 60 pn 02 70 lq 89 80 h

variational bounds for the generalized random energy model we compute the pressure of the random energy model rem and generalized random energy model grem by establishing variational upper and lower bounds for the upper bound we generalize guerra s broken replica symmetry bounds and identify the random probability cascade as the appropriate random overlap structure for the model for the rem the lower bound is obtained in the high temperature regime using talagrand s concentration of measure inequality and in the low temperature regime using convexity and the high temperature formula the lower bound for the grem follows from the lower bound for the rem by induction while the argument for the lower bound is fairly standard our proof of the upper bound is new

a comment on a simple test for neglected heterogeneity in panel studies a recently proposed test for unmeasured heterogeneity hamerle 1990 biometrics 46 193 199 has the merit of being relatively convenient to compute due to the extremely simple form of the variance estimator employed it is argued that this variance estimator is inconsistent in that it asymptotically overestimates the true variance this renders the test procedure as described by hamerle asymptotically undersized

test of homogeneity of binary data with explanatory variables summary apparent heterogeneity of the risk of a disease in different groups may be explained by subjectspecific risk factors unequally distributed in these groups we propose a score test of homogeneity that allows adjustment for known risk factors of the disease the test is based oni a random effect logistic regression model and requires only simple computations in addition to a conventional logistic regression method the score test is applied to the study of geographical heterogeneity of cognitive impairment in elderly using a sample of 3 318 subjects scattered in 75 parishes it is shown that an apparent heterogeneity disappears when taking into account subject specific risk factors this test may also be useful for studying familial aggregation of a disease testing homogeneity of the distribution of binary traits in different groups has long been recognized as an important problem particularly in conventional genetics smith 1951 and in genetic epidemiology where it may be used to investigate the familial aggregation of a disease the presence of familial aggregation suggests a genetic determinant testing homogeneity of geographical units is also of interest the presence of heterogeneity suggests the presence of an unmeasured environmental factor another application occurs if the possible correlation of the data is treated as a nuisance it is useful to test whether the groups are homogeneous before performing ordinary regression models liang 1987 chi squared tests are used for testing homogeneity when the number of groups is small however the chi squared test is not applicable when the sizes of the groups are not large haldane 1940 and when the number of groups is large in such cases random effect models are preferred the probability of disease within a group have a common distribution thus the null hypothesis is specified by a null variance of the random effect and alternative hypotheses are specified by a unique parameter the variance of the random effect whatever the number of groups see potthoff and whittinghill 1966 wisniewsky 1968 and tarone 1979 in epidemiologic studies however we often need to test for homogeneity while adjusting for other risk factors of the disease indeed risk factors if differently distributed in the different groups may play the role of confounding factors relative to the group effect it is of paramount importance in genetic studies to investigate whether an apparent familial aggregation may be explained by nongenetic factors such as educational level or nutritional habits which may also segregate in families similarly geographical clusters may be explained by nonenvironmental factors unequally distributed in the geographical units based on a random effect logistic regression model we derive a score test of homogeneity that allows adjustment on explanatory variables the score statistic is the same as that proposed by hamerle 1990 in the context of repeated measurements but the variance proposed in the present paper is different simulations show that it leads to a more powerful test we use this test to investigate the possible geographical heterogeneity of cognitive impairment as measured by the mini mental state score in 3 318 subjects scattered in 75 parishes in southwestern france

power counting theorem for non local matrix models and renormalisation solving the exact renormalisation group equation a la wilson polchinski perturbatively we derive a power counting theorem for general matrix models with arbitrarily non local propagators the power counting degree is determined by two scaling dimensions of the cut off propagator and various topological data of ribbon graphs as a necessary condition for the renormalisability of a model the two scaling dimensions have to be large enough relative to the dimension of the underlying space in order to have a renormalisable model one needs additional locality properties typically arising from orthogonal polynomials which relate the relevant and marginal interaction coefficients to a finite number of base couplings the main application of our power counting theorem is the renormalisation of field theories on noncommutative d in matrix formulation