morphisms of f isocrystals and the finite monodromy theorem for unit root f isocrystals we discuss tate type problems for f isocrystals that is the full faithfulness of the natural restriction functors between categories of overconvergent f isocrystals on schemes of positive characteristic we prove it in the cases of unit root f isocrystals using this result we prove that an overconvergent unit root f isocrystal has a finite monodromy

shift in the velocity of a front due to a cutoff we consider the effect of a small cutoff ensuremath varepsilon on the velocity of a traveling wave in one dimension simulations done over more than ten orders of magnitude as well as a simple theoretical argument indicate that the effect of the cutoff ensuremath varepsilon is to select a single velocity that converges when ensuremath varepsilon ensuremath rightarrow 0 to the one predicted by the marginal stability argument for small ensuremath varepsilon the shift in velocity has the form k mathrm ln ensuremath varepsilon ensuremath 2 and our prediction for the constant k agrees very well with the results of our simulations a very similar logarithmic shift appears in more complicated situations in particular in finite size effects of some microscopic stochastic systems our theoretical approach can also be extended to give a simple way of deriving the shift in position due to initial conditions in the fisher kolmogorov or similar equations

recovery thresholds in the sparse planted matching problem we consider the statistical inference problem of recovering an unknown perfect matching hidden in a weighted random graph by exploiting the information arising from the use of two different distributions for the weights on the edges inside and outside the planted matching a recent work has demonstrated the existence of a phase transition in the large size limit between a full and a partial recovery phase for a specific form of the weights distribution on fully connected graphs we generalize and extend this result in two directions we obtain a criterion for the location of the phase transition for generic weights distributions and possibly sparse graphs exploiting a technical connection with branching random walk processes as well as a quantitatively more precise description of the critical regime around the phase transition

effect of noise on spinodal decomposition the long time behaviour of two dimensional systems undergoing spinodal decomposition is studied numerically with the aid of a cell dynamical approach both without and with noise in both cases the representative length scale of the pattern behaves as l t approximately tphi where the exponent phi crosses over from approximately 0 28 to approximately 0 33 the crossover time increases with an increase in amplitude of the noise

adiabatic liouvillean in the theory of diffusion limited recombination i a regular method of deriving the governing adiabatic liouvillean on a lattice for a many body system of locally and instantaneously recombining particles in reaction a b to 0 is described when the rate u of the recombination tends to infinity u to infinity the local reaction liouvillean is shown to be replaced with a non local operator involving renormalized matrix elements which are proportional to slow diffusive jump rates properties of the new liouvillean are described quantum field formalism is employed

overholonomicity of overconvergent f isocrystals over smooth varieties we prove the overholonomicity of overconvergent f isocrystals over smooth varieties this implies that the notions of overholonomicity and devissability in overconvergent f isocrystals are equivalent then the overholonomicity is stable under tensor products so the overholonomicity gives a p adic cohomology stable under grothendieck s cohomological operations

non algebraic domain growth for phase ordering dynamics in a random field discusses the three stage numerical exposition of the effects of quenched disorder on phase ordering dynamics the authors study the effects of random fields on domain growth the numerical results indicate that the domain growth law is logarithmic for both the cases with non conserve and conserved order parameter this is compatible with theoretical expectations they also study the dynamical scaling of the structure factor for both the non conserved and conserved cases

fluctuating fronts as correlated extreme value problems an example of gaussian statistics in this paper we view fluctuating fronts made of particles on a one dimensional lattice as an extreme value problem the idea is to denote the configuration for a single front realization at time t by the set of co ordinates k i t identical with k 1 t k 2 t k n t t of the constituent particles where n t is the total number of particles in that realization at time t when k i t are arranged in the ascending order of magnitudes the instantaneous front position can be denoted by the location of the rightmost particle i e by the extremal value k f t max k 1 t k 2 t k n t t due to interparticle interactions k i t at two different times for a single front realization are naturally not independent of each other and thus the probability distribution p k f t based on an ensemble of such front realizations describes extreme value statistics for a set of correlated random variables in view of the fact that exact results for correlated extreme value statistics are rather rare here we show that for a fermionic front model in a reaction diffusion system p k f t is gaussian in a bosonic front model however we observe small deviations from the gaussian

polymers on disordered hierarchical lattices a nonlinear combination of random variables the problem of directed polymers on disordered hierarchical and hypercubic lattices is considered for the hierarchical lattices the problem can be reduced to the study of the stable laws for combining random variables in a nonlinear way we present the results of numerical simulations of two hierarchical lattices finding evidence of a phase transition in one case for a limiting case we extend the perturbation theory developed by derrida and griffiths to nonzero temperature and to higher order and use this approach to calculate thermal and geometrical properties overlaps of the model in this limit we obtain an interpolation formula allowing one to obtain the noninteger moments of the partition function from the integer moments we obtain bounds for the transition temperature for hierarchical and hypercubic lattices and some similarities between the problem on the two different types of lattice are discussed

directed polymers on trees a martingale approach the authors use martingale methods and simple convexity arguments to compute rigorously the limiting free energy in the problem of directed polymers on a tree the limit is a degenerate random variable and convergence holds almost surely the only assumption on the common distribution of the random potentials attached to the bonds of the tree is that its laplace transform exists everywhere in 0 infinity

f isocristaux surconvergents et surcoherence differentielle soient mathcal v un anneau de valuation discrete complet d inegales caracteristiques de corps residuel parfait k mathcal p un mathcal v schema formel propre et lisse t un diviseur de la fibre speciale p de mathcal p u l ouvert de p complementaire de t y un sous k schema ferme lisse de u nous prouvons que la categorie des f isocristaux surconvergents sur y est equivalente a celle des f isocristaux surcoherents sur y voir car 6 2 1 et 6 4 3 a plus generalement nous etablissons par recollement une telle equivalence pour tout k schema separe lisse y nous verifions de plus que les f complexes de mathcal d dag mathcal p phantom dag t mathbb q modules a cohomologie bornee et mathcal d dag mathcal p phantom dag t mathbb q surcoherente se devissent en f isocristaux surconvergents

extremal paths on a random cayley tree we investigate the statistics of extremal path s both the shortest and the longest from the root to the bottom of a cayley tree the lengths of the edges are assumed to be independent identically distributed random variables drawn from a distribution rho l besides the number of branches from any node is also random exact results are derived for arbitrary distribution rho l in particular for the binary 0 1 distribution rho l pdelta l 1 1 p delta l 0 we show that as p increases the minimal length undergoes an unbinding transition from a localized phase to a moving phase at the critical value p p c 1 b 1 where b is the average branch number of the tree as the height n of the tree increases the minimal length saturates to a finite constant in the localized phase p p c where the velocity v min p is determined via a front selection mechanism at p p c the minimal length grows with n in an extremely slow double logarithmic fashion the length of the maximal path on the other hand increases linearly as v max p n for all p the maximal and minimal velocities satisfy a general duality relation v min p v max 1 p 1 which is also valid for directed paths on finite dimensional lattices

extreme values and fat tails of multifractal fluctuations in this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process we also study the heavy power law tail behavior of probability density function associated with such data we show that because of strong correlations the standard extreme value approach is not valid and classical tail exponent estimators should be interpreted cautiously extreme statistics associated with multifractal random processes turn out to be characterized by non self averaging properties our considerations rely upon some analogy between random multiplicative cascades and the physics of disordered systems and also on recent mathematical results about the so called multifractal formalism applied to financial time series our findings allow us to propose an unified framework that accounts for the observed multiscaling properties of return fluctuations the volatility clustering phenomenon and the observed inverse cubic law of the return pdf tails

non algebraic domain growth in binary alloys with quenched disorder the authors present detailed numerical results from a computationally efficient cell dynamical system model of domain growth in binary alloys with quenched disorder their numerical results suggest that the domain growth law for the disordered case is compatible with r t approximately 1nt x where x has a weak dependence on the disorder amplitude however it is possible that their simulations do not access the true asymptotic regime they also find that the scaled structure factor for the disordered case is independent of the amplitude of disorder and is the same as that for the pure system

extreme value statistics of hierarchically correlated variables deviation from gumbel statistics and anomalous persistence we study analytically the distribution of the minimum of a set of hierarchically correlated random variables e1 e2 ellipsis e n where e i represents the energy of the ith path of a directed polymer on a cayley tree if the variables were uncorrelated the minimum energy would have an asymptotic gumbel distribution we show that due to the hierarchical correlations the forward tail of the distribution of the minimum energy becomes highly nonuniversal depends explicitly on the distribution of the bond energies epsilon and is generically different from the superexponential forward tail of the gumbel distribution the consequence of these results to the persistence of hierarchically correlated random variables is discussed and the persistence is also shown to be generically anomalous

image directe superieure et unipotence let x be a proper smooth curve over a perfect field of characteristic p 0 and u an open dense subscheme of x we prove that convergent f isocrystals on u are overconvergent under the condition that they are overconvergent at each point in x nu using this criterion we show that the higher direct images rfcrys ov by a proper smooth morphism of schemes f v u are overconvergent introduction soient u k une courbe a ne et lisse sur un corps parfait de caracteristique p 0 x k une compactification lisse de u et f v u un morphisme propre et lisse en utilisant un critere de surconvergence dont l idee initiale revient a de jong cf 9 et gr ce aux resultats locaux de kedlaya 13 nous montrons que les images directes superieures rf ov sont surconvergentes repondant ainsi dans le cas d une courbe a ne et lisse a une conjecture de 3 en particulier leurs groupes de cohomologie sont de dimension finie et verifient la dualite de poincare enfin nous montrons que le theoreme de monodromie p adique local de 1 14 et 17 permet de deduire que tout f isocristal surconvergent sur u provient apres une eventuelle extension finie etale d un f log isocristal nous remercions kiran kedlaya pour nous avoir indique comment obtenir des resultats de descente de modules via ses lemmes de factorisations de matrices a notations soit k un corps parfait de caracteristique p on note w l anneau des vecteurs de witt de k ok une extension finie de w et k0 respectivement k le corps des fractions de w resp ok on suppose le corps k muni d un frobenius s relevant le frobenius canonique de k0 pour une indeterminee t on notera s 1 4 ok 1 21 2t nok k a 1 4 py i1 40 ait i ai a k jaijr i 0 i y pour tout 0 r 1 h 1 4 a 1 4 p y i1 40 ait i ai a k jaij 0 i y hy 1 4 a a h jaijr 0 i y pour un certain 0 r 1

on a discrete model of phase separation dynamics a spatially discrete model for phase separation with conserved order parameter is proposed this one dimensional model is obtained as the deterministic limit of an anisotropic lattice gas a particular choice is made for the jump rates which still fulfill detailed balance conditions so that the resulting model is mathematically tractable it exhibits a phase transition of first order type whose nonlinear dynamics is investigated using both analytical and numerical methods all the stationary solutions with zero current are found and parametrized in terms of jacobian elliptic functions showing a striking similarity with the nonlinear continuous cahn hilliard equation in the limit of infinite wavelength particular solutions are found which descrive isolated domains of arbitrary size embedded in an homogeneous infinite medium of the opposite phase new results are also presented on the structure of the set of solutions time dependent profiles are studied in the spinodal regime and the stability of bounded stationary solutions is also investigated in this context a description of time dependent profiles is proposed which considers only interactions between neighboring domains and makes use of isolated domain solutions this approach results in an analytic expression for the exponents characteristic of the instability of stationary solutions and is validated by comparison to numerical values qualitative results are also discussed and the relation to the cahn hilliard equation is emphasized

finite size effects in random energy models and in the problem of polymers in a random medium by the use of traveling wave equations we calculate the finite size corrections to the free energy of random energy models in their low temperature phases and in the neighborhood of the transition temperature we find that although the extensive part of the free energy does not show any critical behavior when the temperature approaches its transition value the finite size corrections signal the transition by becoming singular we obtain a scaling form for these finite size corrections valid in the limitn andt t c by considering a generalized random energy model in the limit of a very large number of steps we obtain results for the finite size corrections in the problem of a polymer in a random medium

anderson transition on the cayley tree as a traveling wave critical point for various probability distributions for anderson localization on the cayley tree we study the statistics of various observables as a function of the disorder strength w and the number n of generations we first consider the landauer transmission tn in the localized phase its logarithm follows the traveling wave form where i the disorder averaged value moves linearly and the localization length diverges as with loc 1 and ii the variable t is a fixed random variable with a power law tail p t 1 t 1 w for large t with 0 w 1 2 so that all integer moments of tn are governed by rare events in the delocalized phase the transmission tn remains a finite random variable as n and we measure near criticality the essential singularity with t 0 25 we then consider the statistical properties of normalized eigenstates x x 2 1 in particular the entropy s x x 2ln x 2 and the inverse participation ratios ipr iq x x 2q in the localized phase the typical entropy diverges as with s 1 5 whereas it grows linearly as styp n n in the delocalized phase finally for the ipr we explain how closely related variables propagate as traveling waves in the delocalized phase in conclusion both the localized phase and the delocalized phase are characterized by the traveling wave propagation of some probability distributions and the anderson localization delocalization transition then corresponds to a traveling non traveling critical point moreover our results point toward the existence of several length scales that diverge with different exponents at criticality

pleine fidelite sans structure de frobenius et isocristaux partiellement surconvergents soit mathcal v un anneau de valuation discrete complet d inegales caracteristiques 0 p de corps residuel parfait k de corps des fractions k soient x une variete sur k y un ouvert de x nous prolongeons le theoreme de pleine fidelite de kedlaya de la maniere suivante en effet nous ne supposons pas y lisse le foncteur canonique f text mathrm isoc dag y x k to f text mathrm isoc dag y y k est pleinement fidele supposons a present y lisse nous construisons la categorie mathrm isoc dag dag y x k des isocristaux partiellement surcoherents sur y x dont les objets sont certains mathcal d modules arithmetiques de plus nous verifions l equivalence de categories rm sp y x mathrm isoc dag y x k cong mathrm isoc dag dag y x k

critical weight statistics of the random energy model and of the directed polymer on the cayley tree we consider the critical point of two mean field disordered models i the random energy model rem introduced by derrida as a mean field spin glass model of n spins and ii the directed polymer of length n on a cayley tree dpct with random bond energies both models are known to exhibit a freezing transition between a high temperature phase where the entropy is extensive and a low temperature phase of finite entropy where the weight statistics coincides with the weight statistics of l evy sums with index ensuremath mu t t c l1 in this paper we study the weight statistics at criticality via the entropy s ensuremath ensuremath sum w i phantom rule 0 2em 0ex mathrm ln phantom rule 0 2em 0ex w i and the generalized moments y k ensuremath sum w i k where the w i are the boltzmann weights of the 2 n configurations in the rem we find that the critical weight statistics is governed by the finite size exponent ensuremath nu 2 the entropy scales as overline s n t c ensuremath sim n 1 2 the typical values e overline mathrm ln phantom rule 0 2em 0ex y k decay as n ensuremath k 2 and the disorder averaged values overline y k are governed by rare events and decay as n ensuremath 1 2 for any kg1 for the dpct we find that the entropy scales similarly as overline s n t c ensuremath sim n 1 2 whereas another exponent ensuremath nu ensuremath 1 governs the y k statistics the typical values e overline mathrm ln phantom rule 0 2em 0ex y k decay as n ensuremath k and the disorder averaged values overline y k decay as n ensuremath 1 for any kg1 as a consequence the asymptotic probability distribution overline ensuremath pi n ensuremath infty q of the overlap q in addition to the delta function ensuremath delta q which bears the whole normalization contains an isolated point at q 1 as a memory of the delta peak 1 ensuremath t t c ensuremath delta q ensuremath 1 of the low temperature phase tl t c the associated value overline ensuremath pi n ensuremath infty q 1 is finite for the dpct and diverges as overline ensuremath pi n ensuremath infty q 1 ensuremath sim n 1 2 for the rem

contest based on a directed polymer in a random medium we introduce a simple one parameter game derived from a model describing the properties of a directed polymer in a random medium at his turn each of the two players picks a move among two alternatives in order to maximize his final score and minimize opponent s return for a game of length n we find that the probability distribution of the final score s n develops a traveling wave form rm prob s n m f m v n with the wave profile f z unusually decaying as a double exponential for large positive and negative z in addition as the only parameter in the game is varied we find a transition where one player is able to get his maximum theoretical score by extending this model we suggest that the front velocity v is selected by the nonlinear marginal stability mechanism arising in some traveling wave problems for which the profile decays exponentially and for which standard traveling wave theory applies

searching for an optimal path in a tree with random costs we consider the problem of finding an optimal path leading from the root of a tree to any of its leaves the tree is known to be uniform binary and of height n and each branch independently may have a cost of 1 or 0 with probability p and 1 p respectively we show that for p 1 2 every algorithm which guarantees finding an exact cheapest path or even a path within a fixed cost ratio of the cheapest must run in exponential average time if however we are willing to accept a near optimal solution almost always then a pruning algorithm exists which finds such a solution in linear expected time the algorithm employs a depth first strategy which stops at regular intervals to appraise its progress and if the progress does not meet a criterion based on domain specific knowledge the current node is irrevocably pruned

theory of weights in p adic cohomology let k be a finite field of characteristic p 0 we construct a theory of weights for overholonomic complexes of arithmetic d modules with frobenius structure on varieties over k the notion of weight behave like deligne s one in the adic framework first the six operations preserve weights and secondly the intermediate extension of an immersion preserves pure complexes and weights this is joint work with tomoyuki abe

random convex hulls and extreme value statistics in this paper we study the statistical properties of convex hulls of n random points in a plane chosen according to a given distribution the points may be chosen independently or they may be correlated after a non exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem we present a unifying approach based on the notion of support function of a closed curve and the associated cauchy s formulae that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics as an example of correlated points we study here in detail the case when the points represent the vertices of n independent random walks in the continuum time limit this reduces to n independent planar brownian trajectories for which we compute exactly for all n the mean perimeter and the mean area of their global convex hull our results have relevant applications in ecology in estimating the home range of a herd of animals some of these results were announced recently in a short communication phys rev lett 103 140602 2009

ground state energy anisotropy for directed polymers in random media the orientation dependence of the line energy of zero temperature directed polymers is studied analytically and numerically for the two dimensional square lattice with site disorder using the equivalence to single step growth models the exact line energy of maximum energy paths is computed for exponential and geometric disorder distributions the resulting expression depends on the distributions only through their mean and variance a universal square root singularity appears in the ground state energy as the line orientation approaches the edges of the wedge shaped lattice we also discuss the relationship between point to point and point to line optimization problems as well as their connection to the classic wulff construction for crystal shapes in addition we derive some general distribution independent properties of the optimal path angle in the point to line configuration this angle is argued to be directly measurable in fracture experiments of anisotropic materials such as paper

two repulsive lines on disordered lattices we investigate the ground state properties of two lines with on site repulsion on disordered cayley tree and berker hierarchical lattices in connection with the question of multiple pure states for the corresponding one line problem exact recursion relations for the distribution of ground state energies and of the overlaps are derived based on a numerical study of the recursion relations we establish that the total interaction energy on average is asymptotically proportional to the width of the ground state energy fluctuation of a single line for both weak and strong i e hard core repulsion when the lengtht of the lines is finite there is a finite probability of ordert a for nearly degenerate nonoverlapping one line ground state configurations in which case the interaction energy vanishes we show thata t on hierarchical lattices monte carlo transfer matrix calculation on a 1 1 dimensional model yields the same scaling for the interaction energy but ana different from 1 3 finitelength scalings of the distribution of the interaction energy and of the overlap are also discussed

crossing intervals of non markovian gaussian processes we review the properties of time intervals between the crossings at a level m of a smooth stationary gaussian temporal signal the distribution of these intervals and the persistence are derived within the independent interval approximation iia these results grant access to the distribution of extrema of a general gaussian process exact results are obtained for the persistence exponents and the crossing interval distributions in the limit of large m in addition the small time behavior of the interval distributions and the persistence is calculated analytically for any m the iia is found to reproduce most of these exact results and its accuracy is also illustrated by extensive numerical simulations applied to non markovian gaussian processes appearing in various physical contexts

linearization effect in multifractal analysis insights from the random energy model abstract the analysis of the linearization effect in multifractal analysis and hence of the estimation of moments for multifractal processes is revisited borrowing concepts from the statistical physics of disordered systems notably from the analysis of the so called random energy model considering a standard multifractal process compound poisson motion chosen as a simple representative example we show the following i the existence of a critical order q beyond which moments though finite cannot be estimated through empirical averages irrespective of the sample size of the observation ii multifractal exponents necessarily behave linearly in q for q q tailoring the analysis conducted for the random energy model to that of compound poisson motion we provide explicative and quantitative predictions for the values of q and for the slope controlling the linear behavior of the multifractal exponents these quantities are shown to be related only to the definition of the multifractal process and not to depend on the sample size of the observation monte carlo simulations conducted over a large number of large sample size realizations of compound poisson motion comfort and extend these analyses

finite local monodromy of overconvergent unit root f isocrystals on a curve we prove that the category of p adic continuous representations of a fundamental group of a curve over a perfect field of a positive characteristic p with finite local monodromy is equivalent to that of overconvergent unit root f isocrystals on the curve to show the equivalence of categories we study the local theory and apply it to the global case

nonuniversality and analytical continuation in moments of directed polymers on hierarchical lattices we prove the moments of the directed polymer partition function gz using an exact position space renormalization group scheme on a hierarchical lattice after sufficient iteration the characteristic functionf n ln gzn of the probability z converges to a stable limitf n for smalln the limiting behavior is independent of the initial distribution while for largen f n is completely determined by it and is thus nonuniversal there is a smooth crossover between the two regimes for small effective dimensions and the nonlinear behavior of the small moments can be used to extract information on the universal scaling properties of the distribution for large effective dimensions there is a sharp transition between the two regimes and analytical continuation from integer moments ton 0 is not possible replica arguments can account for most features of the observed results