Symmetric random walks on Homeo+(R)

We study symmetric random walks on finitely generated groups of orientation-preserving homeomorphisms of the real line. We establish an oscillation property for the induced Markov chain on the line that implies a weak form of recurrence. Except for a few special cases, which can be treated separately, we prove a property of "global stability at a finite distance": roughly speaking, there exists a compact interval such that any two trajectories get closer and closer whenever one of them returns to the compact interval. The probabilistic techniques employed here lead to interesting results for the study of group actions on the line. For instance, we show that under a suitable change of the coordinates, the drift of every point becomes zero provided that the action is minimal. As a byproduct, we recover the fact that every finitely generated group of homeomorphisms of the real line is topologically conjugate to a group of (globally) Lipschitz homeomorphisms. Moreover, we show that such a conjugacy may be chosen in such a way that the displacement of each element is uniformly bounded

The Pressure of Hot g2ϕ4g^2 \phi^4 Theory at order g5g^5

The order $g^5$ contribution to the pressure of massless $g^2 \phi^4$ theory at nonzero temperature is obtained explicitly. Lower order contributions are reconsidered and two issues leading to the optimal choice of rearranged Lagrangian for such calculations are clarified.Comment: 15 pages, Latex, postscript file attached at the en

Integrable Hierarchies and Information Measures

In this paper we investigate integrable models from the perspective of information theory, exhibiting various connections. We begin by showing that compressible hydrodynamics for a one-dimesional isentropic fluid, with an appropriately motivated information theoretic extension, is described by a general nonlinear Schrodinger (NLS) equation. Depending on the choice of the enthalpy function, one obtains the cubic NLS or other modified NLS equations that have applications in various fields. Next, by considering the integrable hierarchy associated with the NLS model, we propose higher order information measures which include the Fisher measure as their first member. The lowest members of the hiearchy are shown to be included in the expansion of a regularized Kullback-Leibler measure while, on the other hand, a suitable combination of the NLS hierarchy leads to a Wootters type measure related to a NLS equation with a relativistic dispersion relation. Finally, through our approach, we are led to construct an integrable semi-relativistic NLS equation.Comment: 11 page

On the screening of static electromagnetic fields in hot QED plasmas

We study the screening of static magnetic and electric fields in massless quantum electrodynamics (QED) and massless scalar electrodynamics (SQED) at temperature $T$. Various exact relations for the static polarisation tensor are first reviewed and then verified perturbatively to fifth order (in the coupling) in QED and fourth order in SQED, using different resummation techniques. The magnetic and electric screening masses squared, as defined through the pole of the static propagators, are also calculated to fifth order in QED and fourth order in SQED, and their gauge-independence and renormalisation-group invariance is checked. Finally, we provide arguments for the vanishing of the magnetic mass to all orders in perturbation theory.Comment: 37 pages, 8 figure

The Free Energy Of Hot Gauge Theories

The total perturbative contribution to the free-energy of hot SU(3) gauge theory is argued to lie significantly higher than the full result obtained by lattice simulations. This then suggests the existence of large non-perturbative corrections even at temperatures a few times above the critical temperature. Some speculations are then made on the nature and origin of the non-perturbative corrections. The analysis is then carried out for quantum chromodynamics, $SU(N_c)$ gauge theories, and quantum electrodynamics, leading to a conjecture and one more speculation.Comment: Revised Journal version;25 pages Latex and 11 .eps figures in separate file. Requires epsf.st

Solution to the 3-loop Φ\Phi-derivable Approximation for Scalar Thermodynamics

We solve the 3-loop $\Phi$-derivable approximation to the thermodynamics of the massless $\phi^4$ field theory by reducing it to a 1-parameter variational problem. The thermodynamic potential is expanded in powers of $g^2$ and $m/T$, where $g$ is the coupling constant, $m$ is a variational mass parameter, and $T$ is the temperature. There are ultraviolet divergences beginning at 6th order in $g$ that cannot be removed by renormalization. However the finite thermodynamic potential obtained by truncating after terms of 5th order in $g$ and $m/T$ defines a stable approximation to the thermodynamic functions.Comment: 4 pages, 1 figur

Ewing Sarcoma/Primitive Neuroectodermal Tumor of the Kidney: Two Unusual Presentations of a Rare Tumor

Only few cases of primary renal Ewing's sarcoma have been reported in the literature to date. We present here two cases of renal ES/PNET with an uncanny presentation. The first case was discovered after the patient presented clinically with irradiating flank pain, mimicking the pain related with kidney stones. The second case had clinical presentation of pulmonary thromboembolism after the patient was involved in an automobilist accident. The tumors were mainly composed of small blue cells which by immunohistochemical were positive for neural markers, and FISH revealed the translocation 22q12 for the EWSR1 gene. The diagnosis of renal primitive neuroectodermal tumor/EWING tumor is very rare and usually involves several different diagnostic techniques. The differential diagnosis is usually broad with frequent overlapping features between the entities. The cases presented in this paper illustrated the difficulties with which routine anatomical pathologist is faced when dealing with rare renal poorly differentiated neoplasm in adults

The Free Energy of High Temperature QED to Order e5e^{5} From Effective Field Theory

Massless quantum electrodynamics is studied at high temperature and zero chemical potential. We compute the Debye screening mass to order $e^{4}$ and the free energy to order $e^{5}$} by an effective field theory approach, recently developed by Braaten and Nieto. Our results are in agreement with calculations done in resummed perturbation theory. This method makes it possible to separate contributions to the free energy from different momentum scales (order $T$ and $eT$) and provides an economical alternative to computations in the full theory which involves the dressing of internal propagators.Comment: 10 pages Latex, 6 figure

Gap equation in scalar field theory at finite temperature

We investigate the two-loop gap equation for the thermal mass of hot massless $g^2\phi^4$ theory and find that the gap equation itself has a non-zero finite imaginary part. This indicates that it is not possible to find the real thermal mass as a solution of the gap equation beyond $g^2$ order in perturbation theory. We have solved the gap equation and obtain the real and the imaginary part of the thermal mass which are correct up to $g^4$ order in perturbation theory.Comment: 13 pages, Latex with axodraw, Minor corrections, Appendix adde