exact solution of return hysteresis loops in a one dimensional random field ising model at zero temperature minor hysteresis loops within the main loop are obtained exactly in the one dimensional ferromagnetic random field ising model at zero temperature numerical simulations of the model show excellent agreement with the exact results

improved belief propagation algorithm finds many bethe states in the random field ising model on random graphs we first present an empirical study of the belief propagation bp algorithm when run on the random field ising model defined on random regular graphs in the zero temperature limit we introduce the notion of extremal solutions for the bp equations and we use them to fix a fraction of spins in their ground state configuration at the phase transition point the fraction of unconstrained spins percolates and their number diverges with the system size this in turn makes the associated optimization problem highly non trivial in the critical region using the bounds on the bp messages provided by the extremal solutions we design a new and very easy to implement bp scheme which is able to output a large number of stable fixed points on one hand this new algorithm is able to provide the minimum energy configuration with high probability in a competitive time on the other hand we found that the number of fixed points of the bp algorithm grows with the system size in the critical region this unexpected feature poses new relevant questions about the physics of this class of models

one dimensional random field ising model gibbs states and structure of ground states we consider the random gibbs field formalism for the ferromagnetic id dichotomous random field ising model as the simplest example of a quenched disordered system we prove that for nonzero temperatures the gibb state is unique for any realization of the external field then we prove that ast 0 the gibbs state converges to a limit a ground state for almost all realizations of the external field the ground state turns out to be a probability measure concentrated on an infinite set of configurations and we give a constructive description of this measure

zero temperature hysteresis in an anti ferromagnetic ising chain with quenched random fields abstract we discuss the non equilibrium dynamics of an anti ferromagnetic ising chain in a quenched random field our discussion is mainly in the context of magnetic hysteresis but its relation to the problem if random sequential adsorption is also noted

bethe lattice spin glass the effects of a ferromagnetic bias and external fields i bifurcation analysis we present a rigorous analysis of the j ising spin glass model on the bethe lattice with fixed uncorrelated boundary conditions phase diagrams are derived as a function of temperature vs concentration of ferromagnetic bonds and for a symmetric distribution of bonds external field vs temperature in this part we characterize the bulk ordered phases using bifurcation theory we prove the existence of a distribution of single site magnetizations far inside the lattice which is stable with respect to changes in the boundary conditions

a mean field spin glass with short range interactions we formulate and study a spin glass model on the bethe lattice appropriate boundary fields replace the traditional self consistent methods they give our model well defined thermodynamic properties we establish that there is a spin glass transition temperature above which the single site magnetizations vanish and below which the edwards anderson order parameter is strictly positive in a neighborhood below the transition temperature we use bifurcation theory to establish the existence of a nontrivial distribution of single site magnetizations two properties of this distribution are studied the leading perturbative correction to the gaussian scaling form at the transition and the nonperturbative behavior of the tails

duality and operator algebras automatic weak continuity and applications abstract we investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras and give several applications of the surprising fact that certain maps are always weak continuous on dual spaces in particular if x is a subspace of a c algebra a and if a a satisfies ax x then we show that the function x ax on x is automatically weak continuous if either a x is a dual operator space or b a x x and x is a dual banach space these results hinge on a generalization to banach modules of tomiyama s famous theorem on contractive projections onto a c subalgebra applications include a new characterization of the weakly closed possibly nonunital and nonselfadjoint operator algebras and a generalization of the theory of w modules to the framework of modules over such algebras we also give a banach module characterization of weakly closed spaces of operators which are invariant under the action of a von neumann algebra

graph partitioning and dilute spin glasses the minimum cost solution the authors calculate the ground state cost function energy for graph bipartitioning and spin glasses on networks with fixed finite valences allowing a continuous distribution for the effective field compared with previous calculations using a field distribution in integral multiples of the coupling strength j the ground state energy is higher by less than one per cent although the distribution itself is altered drastically

arens regularity of banach algebras and the geometry of banach spaces we show that a banach algebra a such that a has the property v of a pelczynski is arens regular a strong uniqueness property of the extension of the product on a unital c algebra a to a is proved the algebraic structure of the bidual of a c algebra can be obtained through the local reflexivity principle we give examples which show that the results are sharp

on the measurement of economic tail risk this paper attempts to provide a decision theoretic foundation for the measurement of economic tail risk which is not only closely related to utility theory but also relevant to statistical model uncertainty the main result is that the only risk measures that satisfy a set of economic axioms for the choquet expected utility and the statistical property of general elicitability i e there exists an objective function such that minimizing the expected objective function yields the risk measure are the mean functional and value at risk var in particular the median shortfall which is the median of tail loss distribution and is also the var at a higher confidence level we also discuss various approaches of backtesting and their relations to elicitability and co elicitability in particular we show that the co elicitability of var and expected shortfall does not lead to a reliable backtesting method for expected shortfall and there have been only indirect backtesting methods for expected shortfall f

approximately norm unital products on c algebras and a non associative gelfand naimark theorem abstract we describe the non associative products on a c algebra a which convert the banach space of a into a banach algebra having an approximate unit bounded by 1 and determine among them those which are associative as a consequence if such a product p satisfies p a b p b a and p a a a 2 for all a b a and some conjugate linear vector space involution on a then p is associative the proof of the above result involves also a new gelfand naimark type theorem asserting that non associative c algebras defined verbatim as in the associative case but removing associativity are alternative if and only if they have an approximate unit bounded by 1

banach space characterizations of unitaries a survey abstract we survey banach space characterizations of unitary elements of c algebras jb triples and jb algebras in the case of the existence of a pre dual appropriate specializations of these characterizations are also reviewed

irreversible processes with nearest particle rates the author considers a class of processes on an infinite one dimensional lattice wherein sites transform irreversibly from vacant to occupied the transformation rates beta l r depend only on the distances l and r to the nearest occupied sites or particles on the left and right respectively he shows that the kinetics can be determined exactly when beta l r is independent of l or r r from a truncated set of 2r rate equations these solvable models can be extended to include simultaneous transformation of strings of n adjacent sites one can thus generate a general class of continuum cooperative car parking problems as the n to infinity limit of a class solvable lattice models

fat tails var and subadditivity financial institutions rely heavily on value at risk var as a risk measure even though it is not globally subadditive first we theoretically show that the var portfolio measure is subadditive in the relevant tail region if asset returns are multivariate regularly varying thus allowing for dependent returns second we note that var estimated from historical simulations may lead to violations of subadditivity this upset of the theoretical var subadditivity in the tail arises because the coarseness of the empirical distribution can affect the apparent fatness of the tails finally we document a dramatic reduction in the frequency of subadditivity violations by using semi parametric extreme value techniques for var estimation instead of historical simulations

the free energy at t 0 of the spin glass in the case of the continuous distribution of the effective field on the bethe lattice for z 4 5 6 abstract we evaluated the free energy at t 0 of the j random ising model on the bethe lattice of the coordination number z 4 5 6 in the case where the distribution function of the effective field has a continuous distribution by using the method of the integral equation of the effective field

eventual convexity of probability constraints with elliptical distributions probability constraints are often employed to intuitively define safety of given decisions in optimization problems they simply express that a given system of inequalities depending on a decision vector and a random vector is satisfied with high enough probability it is known that even if this system is convex in the decision vector the associated probability constraint is not convex in general in this paper we show that some degree of convexity is still preserved for the large class of elliptical random vectors encompassing for example gaussian or student random vectors more precisely our main result establishes that under mild assumptions eventual convexity holds i e the probability constraint is convex when the safety level is large enough we also provide tools to compute a concrete convexity certificate from nominal problem data our results are illustrated on several examples including the situation of polyhedral systems with random technology matrices and arbitrary covariance structure

exact expressions for minor hysteresis loops in the random field ising model on a bethe lattice at zero temperature we obtain exact expressions for the minor hysteresis loops in the ferromagnetic random field ising model on a bethe lattice at zero temperature in the case when the driving field is cycled infinitely slowly

hysteresis in the antiferromagnetic random field ising model at zero temperature we study hysteresis in antiferromagnetic random field ising model at zero temperature the external field is cycled adiabatically between ensuremath ensuremath infty and ensuremath infty two different distributions of the random field are considered i a uniform distribution of width 2 ensuremath delta centered at the origin and ii a gaussian distribution with average value zero and standard deviation ensuremath sigma in each case the hysteresis loop is determined exactly in one dimension and compared with numerical simulations of the model

zero temperature hysteresis in the random field ising model on a bethe lattice we consider the single spin flip dynamics of the random field ising model on a bethe lattice at zero temperature in the presence of a uniform external field we determine the average magnetization as the external field is varied from to by setting up the self consistent field equations which we show are exact in this case the qualitative behaviour of magnetization as a function of the external field unexpectedly depends on the coordination number z of the bethe lattice for z 3 with a gaussian distribution of the quenched random fields we find no jump in magnetization for any non zero strength of disorder for for weak disorder the magnetization shows a jump discontinuity as a function of the external uniform field which disappears for a larger variance of the quenched field we determine exactly the critical point separating smooth hysteresis curves from those with a jump we have checked our results by monte carlo simulations of the model on three and four coordinated random graphs which for large system sizes give the same results as on the bethe lattice but avoid surface effects altogether

equations of motion approach to the spin 1 2 ising model on the bethe lattice we exactly solve the ferromagnetic spin 1 2 ising model on the bethe lattice in the presence of an external magnetic field by means of the equations of motion method within the green s function formalism in particular such an approach is applied to an isomorphic model of localized fermi particles interacting via an intersite coulomb interaction a complete set of eigenoperators is found together with the corresponding eigenvalues the green s functions and the correlation functions are written in terms of a finite set of parameters to be self consistently determined a procedure is developed that allows us to exactly fix the unknown parameters in the case of a bethe lattice with any coordination number z nonlocal correlation functions up to four points are also provided together with a study of the relevant thermodynamic quantities

the sample autocorrelations of heavy tailed processes with applications to arch we study the sample acvf and acf of a general stationary sequence under a weak mixing condition and in the case that the marginal distributions are regularly varying this includes linear and bilinear processes with regularly varying noise and arch processes their squares and absolute values we show that the distributional limits of the sample acf can be random provided that the variance of the marginal distribution is infinite and the process is nonlinear this is in contrast to infinite variance linear processes if the process has a finite second but infinite fourth moment then the sample acp is consistent with scaling rates that grow at a slower rate than the standard root n consequently asymptotic confidence bands are wider than those constructed in the classical theory we demonstrate the theory in full detail far an arch 1 process