9,512 research outputs found
-algebras associated to -correspondences and applications to mirror quantum spheres
The structure of the -algebras corresponding to even-dimensional mirror
quantum spheres is investigated. It is shown that they are isomorphic to both
Cuntz-Pimsner algebras of certain -correspondences and -algebras of
certain labelled graphs. In order to achieve this, categories of labelled
graphs and -correspondences are studied. A functor from labelled graphs to
-correspondences is constructed, such that the corresponding associated
-algebras are isomorphic. Furthermore, it is shown that
-correspondences for the mirror quantum spheres arise via a general
construction of restricted direct sum.Comment: 27 page
Numerical simulation of nonoptimal dynamic equilibrium models
In this paper we present a recursive method for the computation of dynamic competitive equilibria in models with heterogeneous agents and market frictions. This method is based on a convergent operator over an expanded set of state variables. The fixed point of this operator defines the set of all Markovian equilibria. We study approximation properties of the operator as well as the convergence of the moments of simulated sample paths. We apply our numerical algorithm to two growth models, an overlapping generations economy with money, and an asset pricing model with financial frictions.Econometric models
Spin Foams and Noncommutative Geometry
We extend the formalism of embedded spin networks and spin foams to include
topological data that encode the underlying three-manifold or four-manifold as
a branched cover. These data are expressed as monodromies, in a way similar to
the encoding of the gravitational field via holonomies. We then describe
convolution algebras of spin networks and spin foams, based on the different
ways in which the same topology can be realized as a branched covering via
covering moves, and on possible composition operations on spin foams. We
illustrate the case of the groupoid algebra of the equivalence relation
determined by covering moves and a 2-semigroupoid algebra arising from a
2-category of spin foams with composition operations corresponding to a fibered
product of the branched coverings and the gluing of cobordisms. The spin foam
amplitudes then give rise to dynamical flows on these algebras, and the
existence of low temperature equilibrium states of Gibbs form is related to
questions on the existence of topological invariants of embedded graphs and
embedded two-complexes with given properties. We end by sketching a possible
approach to combining the spin network and spin foam formalism with matter
within the framework of spectral triples in noncommutative geometry.Comment: 48 pages LaTeX, 30 PDF figure
Nearest neighbor Markov dynamics on Macdonald processes
Macdonald processes are certain probability measures on two-dimensional
arrays of interlacing particles introduced by Borodin and Corwin
(arXiv:1111.4408 [math.PR]). They are defined in terms of nonnegative
specializations of the Macdonald symmetric functions and depend on two
parameters (q,t), where 0<= q, t < 1. Our main result is a classification of
continuous time, nearest neighbor Markov dynamics on the space of interlacing
arrays that act nicely on Macdonald processes.
The classification unites known examples of such dynamics and also yields
many new ones. When t = 0, one dynamics leads to a new integrable interacting
particle system on the one-dimensional lattice, which is a q-deformation of the
PushTASEP (= long-range TASEP). When q = t, the Macdonald processes become the
Schur processes of Okounkov and Reshetikhin (arXiv:math/0107056 [math.CO]). In
this degeneration, we discover new Robinson--Schensted-type correspondences
between words and pairs of Young tableaux that govern some of our dynamics.Comment: 90 pages; 13 figure
Quilted Floer Cohomology
We generalize Lagrangian Floer cohomology to sequences of Lagrangian
correspondences. For sequences related by the geometric composition of
Lagrangian correspondences we establish an isomorphism of the Floer
cohomologies. We give applications to calculations of Floer cohomology,
displaceability of Lagrangian correspondences, and transfer of displaceability
under geometric composition.Comment: minor corrections and updated reference
Endogenous differential information in financial markets
We develop a two period general equilibrium model with incomplete financial markets and differential information. Making endogenous the traditional informational restriction on consumption, we allow agents to obtain information from physical and financial markets. Thus, the investment in financial promises and the trade of commodities in spot markets appear as natural channels to improve the information that an agent has about the realization of future states of nature.Incomplete Markets, Differential information, Enlightening equilibrium.
The Transition Probability of the -TAZRP (-Bosons) with Inhomogeneous Jump Rates
In this paper we consider the -deformed totally asymmetric zero range
process (-TAZRP), also known as the -boson (stochastic) particle system,
on the lattice, such that the jump rate of a particle depends on
the site where it is on the lattice. We derive the transition probability for
an particle process in Bethe ansatz form as a sum of -fold contour
integrals. Our result generalizes the transition probability formula by
Korhonen and Lee for -TAZRP with a homogeneous lattice, and our method
follows the same approach as theirs
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