6,557 research outputs found
Firm-quasi-stability and re-equilibration in matching markets with contracts
We study firm-quasi-stability in the framework of many-to-many matching with
contracts under substitutable preferences. We establish various links between
firm-quasi-stability and stability and give new insights into the existence and
lattice property of stable allocations. Moreover, we show that
firm-quasi-stable allocations appears naturally when the stability of the
market is disrupted by the entry of new firms or the retirement of some
workers, and introduce a generalized deferred acceptance algorithm to show that
the market can regain stability from firm-quasi-stable allocations by a
decentralized process of offers and acceptances.Comment: 30 page
Holographic coherent states from random tensor networks
Random tensor networks provide useful models that incorporate various
important features of holographic duality. A tensor network is usually defined
for a fixed graph geometry specified by the connection of tensors. In this
paper, we generalize the random tensor network approach to allow quantum
superposition of different spatial geometries. We set up a framework in which
all possible bulk spatial geometries, characterized by weighted adjacent
matrices of all possible graphs, are mapped to the boundary Hilbert space and
form an overcomplete basis of the boundary. We name such an overcomplete basis
as holographic coherent states. A generic boundary state can be expanded on
this basis, which describes the state as a superposition of different spatial
geometries in the bulk. We discuss how to define distinct classical geometries
and small fluctuations around them. We show that small fluctuations around
classical geometries define "code subspaces" which are mapped to the boundary
Hilbert space isometrically with quantum error correction properties. In
addition, we also show that the overlap between different geometries is
suppressed exponentially as a function of the geometrical difference between
the two geometries. The geometrical difference is measured in an area law
fashion, which is a manifestation of the holographic nature of the states
considered.Comment: 33 pages, 8 figures. An error corrected on page 14. Reference update
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