11,146 research outputs found
Properties of Linearly Sofic Groups
We consider (projectively) linearly sofic groups, i.e. groups which can be
approximated using (projective) matrices over arbitrary fields, as a
generalization of sofic groups. We generalize known results for sofic groups
and groups which can be approximated with complex matrices, including the fact
that free products of linearly sofic groups (using a fixed field) are linearly
sofic.Comment: 20 page
Banking Supervision in Integrated Financial Markets: Implications for the EU
I analyze the optimal design of banking supervision in the presence of cross-border lending. Cross-border lending could imply that an individual bank failure in one country could trigger negative spillover effects in another country. Such cross-border contagion effects could turn out to be important in the EU because national banking problems could easily spread via the highly integrated interbank market. I show that if benevolent supervisors are accountable only to their own jurisdiction, they will not take cross-border contagion effects into account. Supervisors with such a national mandate fail to implement the optimum from a supranational perspective. In consequence, the probability of a bank failure will be inefficiently high. Against the background of this result, I argue in favor of institutionalizing an EU ”Supervisory Coordination Authority” to which national supervisors are accountable.banking supervision, systemic risk, cross-border contagion
The infinite XXZ quantum spin chain revisited: Structure of low lying spectral bands and gaps
We study the structure of the spectrum of the infinite XXZ quantum spin
chain, an anisotropic version of the Heisenberg model. The XXZ chain
Hamiltonian preserves the number of down spins (or particle number), allowing
to represent it as a direct sum of N-particle interacting discrete
Schr\"odinger-type operators restricted to the fermionic subspace. In the Ising
phase of the model we use this representation to give a detailed determination
of the band and gap structure of the spectrum at low energy. In particular, we
show that at sufficiently strong anisotropy the so-called droplet bands are
separated from higher spectral bands uniformly in the particle number. Our
presentation of all necessary background is self-contained and can serve as an
introduction to the mathematical theory of the Heisenberg and XXZ quantum spin
chains.Comment: 32 pages, 3 figure
Positivity of Lyapunov exponents for Anderson-type models on two coupled strings
We study two models of Anderson-type random operators on two
deterministically coupled continuous strings. Each model is associated with
independent, identically distributed four-by-four symplectic transfer matrices,
which describe the asymptotics of solutions. In each case we use a criterion by
Gol'dsheid and Margulis (i.e. Zariski denseness of the group generated by the
transfer matrices in the group of symplectic matrices) to prove positivity of
both leading Lyapunov exponents for most energies. In each case this implies
almost sure absence of absolutely continuous spectrum (at all energies in the
first model and for sufficiently large energies in the second model). The
methods used allow for singularly distributed random parameters, including
Bernoulli distributions.Comment: 19 page
Traces in monoidal categories
The main result of this paper is the construction of a trace and a trace
pairing for endomorphisms satisfying suitable conditions in a monoidal
category. This construction is a common generalization of the trace for
endomorphisms of dualizable ob jects in a balanced monoidal category and the
trace of nuclear operators on a locally convex topological vector space with
the approximation property
A generalization of Gordon's theorem and applications to quasiperiodic Schr\"odinger operators
We prove a criterion for absence of eigenvalues for one-dimensional
Schr\"odinger operators. This criterion can be regarded as an -version of
Gordon's theorem and it has a broader range of application. Absence of
eigenvalues is then established for quasiperiodic potentials generated by
Liouville frequencies and various types of functions such as step functions,
H\"older continuous functions and functions with power-type singularities. The
proof is based on Gronwall-type a priori estimates for solutions of
Schr\"odinger equations.Comment: 8 page
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