71,971 research outputs found

### The relative dynamics of investment and the current account in the G-7 economies

This paper contributes to the empirics of the intertemporal approach to the current account. We use a cointegrated VAR framework to identify permanent and transitory components of country-specific and global shocks. Our approach allows us to empirically investigate the sensitivity to persistence implied by many forward-looking models and our results shed new light on the excess volatility of investment encountered by Glick and Rogoff (JME 1995). In G7 data, we find the relative current-account and investment response to be in line with the intertemporal approach

### q-Deformed Relativistic Wave Equations

Based on the representation theory of the $q$-deformed Lorentz and Poincar\'e
symmeties $q$-deformed relativistic wave equation are constructed. The most
important cases of the Dirac-, Proca-, Rarita-Schwinger- and Maxwell- equations
are treated explicitly. The $q$-deformed wave operators look structurally like
the undeformed ones but they consist of the generators of a non-commu\-ta\-tive
Minkowski space. The existence of the $q$-deformed wave equations together with
previous existence of the $q$-deformed wave equations together with previous
results on the representation theory of the $q$-deformed Poincar\'e symmetry
solve the $q$-deformed relativistic one particle problem.Comment: 17 Page

### Strong characterizing sequences of countable groups

Andr\'as Bir\'o and Vera S\'os prove that for any subgroup $G$ of \T
generated freely by finitely many generators there is a sequence $A\subset \N$
such that for all \beta \in \T we have ($\|.\|$ denotes the distance to the
nearest integer) $\beta\in G \Rightarrow \sum_{n\in A} \| n \beta\| <
\infty,\quad \quad \quad \beta\notin G \Rightarrow \limsup_{n\in A, n \to
\infty} \|n \beta\| > 0.$ We extend this result to arbitrary countable
subgroups of \T. We also show that not only the sum of norms but the sum of
arbitrary small powers of these norms can be kept small. Our proof combines
ideas from the above article with new methods, involving a filter
characterization of subgroups of \T

### A $N$-uniform quantitative Tanaka's theorem for the conservative Kac's $N$-particle system with Maxwell molecules

This paper considers the space homogenous Boltzmann equation with Maxwell
molecules and arbitrary angular distribution. Following Kac's program, emphasis
is laid on the the associated conservative Kac's stochastic $N$-particle
system, a Markov process with binary collisions conserving energy and total
momentum. An explicit Markov coupling (a probabilistic, Markovian coupling of
two copies of the process) is constructed, using simultaneous collisions, and
parallel coupling of each binary random collision on the sphere of collisional
directions. The euclidean distance between the two coupled systems is almost
surely decreasing with respect to time, and the associated quadratic coupling
creation (the time variation of the averaged squared coupling distance) is
computed explicitly. Then, a family (indexed by $\delta > 0$) of $N$-uniform
''weak'' coupling / coupling creation inequalities are proven, that leads to a
$N$-uniform power law trend to equilibrium of order ${\sim}_{ t \to + \infty}
t^{-\delta}$, with constants depending on moments of the velocity
distributions strictly greater than $2(1 + \delta)$. The case of order $4$
moment is treated explicitly, achieving Kac's program without any chaos
propagation analysis. Finally, two counter-examples are suggested indicating
that the method: (i) requires the dependance on $>2$-moments, and (ii) cannot
provide contractivity in quadratic Wasserstein distance in any case.Comment: arXiv admin note: text overlap with arXiv:1312.225

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