101,743 research outputs found
Eternal Inflation With Non-Inflationary Pocket Universes
Eternal inflation produces pocket universes with all physically allowed vacua
and histories. Some of these pocket universes might contain a phase of
slow-roll inflation, some might undergo cycles of cosmological evolution and
some might look like the galilean genesis or other "emergent" universe
scenarios. Which one of these types of universe we are most likely to inhabit
depends on the measure we choose in order to regulate the infinities inherent
in eternal inflation. We show that the currently leading measure proposals,
namely the global light-cone cut-off and its local counterpart, the causal
diamond measure, as well as closely related proposals, all predict that we
should live in a pocket universe that starts out with a small Hubble rate, thus
favoring emergent and cyclic models. Pocket universes which undergo cycles are
further preferred, because they produce habitable conditions repeatedly inside
each pocket.Comment: 13 pages, 2 figures, v2: replaced with PRD versio
Presidential War Powers as a Two-Level Dynamic: International Law, Domestic Law, and Practice-Based Legal Change
There is a rich literature on the circumstances under which the United Nations Charter or specific Security Council resolutions authorize nations to use force abroad, and there is a rich literature on the circumstances under which the U.S. Constitution and statutory law allows the President to use force abroad. These are largely separate areas of scholarship, addressing what are generally perceived to be two distinct levels of legal doctrine. This Article, by contrast, considers these two levels of doctrine together as they relate to the United States. In doing so, it makes three main contributions. First, it demonstrates striking parallels between the structure of the international and domestic legal regimes governing the use of force, and it explains how this structure tends to incentivize unilateral action. Second, it theorizes that these two bodies of law are interconnected in previously overlooked ways, such that how the executive branch interprets law at one level is informed by the legal context at the other level. Third, it documents these interactions over time for several important components of the law on the use of force and shows that this two-level dynamic has played a significant role in furthering the practice-based expansion of unilateral war powers. The Article concludes by arguing that both scholars and policy-makers seeking to shape the law on the use of force need to take better account of this dynamic
Single File Diffusion of particles with long ranged interactions: damping and finite size effects
We study the Single File Diffusion (SFD) of a cyclic chain of particles that
cannot cross each other, in a thermal bath, with long ranged interactions, and
arbitrary damping. We present simulations that exhibit new behaviors
specifically associated to systems of small number of particles and to small
damping. In order to understand those results, we present an original analysis
based on the decomposition of the particles motion in the normal modes of the
chain. Our model explains all dynamic regimes observed in our simulations, and
provides convincing estimates of the crossover times between those regimes.Comment: 30 pages, 9 figure
Passage of L\'evy Processes across Power Law Boundaries at Small Times
We wish to characterise when a L\'{e}vy process crosses boundaries like
, , in a one or two-sided sense, for small times ; thus,
we enquire when ,
and/or are almost surely (a.s.) finite or infinite. Necessary and
sufficient conditions are given for these possibilities for all values of
. Often (for many values of ), when the limsups are finite
a.s., they are in fact zero, as we show, but the limsups may in some
circumstances take finite, nonzero, values, a.s. In general, the process
crosses one or two-sided boundaries in quite different ways, but surprisingly
this is not so for the case . An integral test is given to
distinguish the possibilities in that case. Some results relating to other
norming sequences for , and when is centered at a nonstochastic
function, are also given
Passage of Lévy Processes across Power Law Boundaries at Small Times
We wish to characterize when a Lévy process Xt crosses boundaries like tκ, κ > 0, in a one- or two-sided sense, for small times t; thus, we inquire when lim.supt↓0 |Xt|/tκ, lim supt↓0, Xt/tκ and/or lim inft↓0 Xt/tκ are almost surely (a.s.) finite or infinite. Necessary and sufficient conditions are given for these possibilities for all values of κ > 0. This completes and extends a line of research, going back to Blumenthal and Getoor in the 1960s. Often (for many values of κ), when the lim sups are finite a.s., they are in fact zero, but the lim sups may in some circumstances take finite, nonzero, values, a.s. In general, the process crosses one- or two-sided boundaries in quite different ways, but surprisingly this is not so for the case κ = 1/2, where a new kind of analogue of an iterated logarithm law with a square root boundary is derived. An integral test is given to distinguish the possibilities in that case.Supported in part by ARC Grants DP0210572 and DP0664603
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