4,674 research outputs found
Criticality in Formal Languages and Statistical Physics
We show that the mutual information between two symbols, as a function of the
number of symbols between the two, decays exponentially in any probabilistic
regular grammar, but can decay like a power law for a context-free grammar.
This result about formal languages is closely related to a well-known result in
classical statistical mechanics that there are no phase transitions in
dimensions fewer than two. It is also related to the emergence of power-law
correlations in turbulence and cosmological inflation through recursive
generative processes. We elucidate these physics connections and comment on
potential applications of our results to machine learning tasks like training
artificial recurrent neural networks. Along the way, we introduce a useful
quantity which we dub the rational mutual information and discuss
generalizations of our claims involving more complicated Bayesian networks.Comment: Replaced to match final published version. Discussion improved,
references adde
Cool Core Bias in Sunyaev-Zel'dovich Galaxy Cluster Surveys
Sunyaev-Zeldovich (SZ) surveys find massive clusters of galaxies by measuring
the inverse Compton scattering of cosmic microwave background off of
intra-cluster gas. The cluster selection function from such surveys is expected
to be nearly independent of redshift and cluster astrophysics. In this work, we
estimate the effect on the observed SZ signal of centrally-peaked gas density
profiles (cool cores) and radio emission from the brightest cluster galaxy
(BCG) by creating mock observations of a sample of clusters that span the
observed range of classical cooling rates and radio luminosities. For each
cluster, we make simulated SZ observations by the South Pole Telescope and
characterize the cluster selection function, but note that our results are
broadly applicable to other SZ surveys. We find that the inclusion of a cool
core can cause a change in the measured SPT significance of a cluster between
0.01% - 10% at z > 0.3, increasing with cuspiness of the cool core and angular
size on the sky of the cluster (i.e., decreasing redshift, increasing mass). We
provide quantitative estimates of the bias in the SZ signal as a function of a
gas density cuspiness parameter, redshift, mass, and the 1.4 GHz radio
luminosity of the central AGN. Based on this work, we estimate that, for the
Phoenix cluster (one of the strongest cool cores known), the presence of a cool
core is biasing the SZ significance high by ~ 6%. The ubiquity of radio
galaxies at the centers of cool core clusters will offset the cool core bias to
varying degrees.Comment: 8 pages, 4 figures, accepted to Ap
The bulk Hilbert space of double scaled SYK
The emergence of the bulk Hilbert space is a mysterious concept in
holography. In arXiv:1811.02584, the SYK model was solved in the double scaling
limit by summing chord diagrams. Here, we explicitly construct the bulk Hilbert
space of double scaled SYK by slicing open these chord diagrams; this Hilbert
space resembles that of a lattice field theory where the length of the lattice
is dynamical and determined by the chord number. Under a calculable
bulk-to-boundary map, states of fixed chord number map to particular entangled
2-sided states with a corresponding size. This bulk reconstruction is
well-defined even when quantum gravity effects are important. Acting on the
double scaled Hilbert space is a Type II algebra of observables, which
includes the Hamiltonian and matter operators. In the appropriate quantum
Schwarzian limit, we also identify the JT gravitational algebra including the
physical SL(2,R) symmetry generators, and obtain explicit representations of
the algebra using chord diagram techniques.Comment: 31 pages, 12 figures; v2-v4: fewer typos, more refs and
clarification
Bootstrap bounds on D0-brane quantum mechanics
We derive simple bootstrap bounds on correlation functions of the BFSS matrix
theory/D0-brane quantum mechanics. The result strengthens and extends
Polchinski's virial theorem bound to finite energies and gives the first
non-trivial bound on . Despite their
simplicity, the bounds hint at some features of the dual black hole geometry.
Our best lower bounds are already a factor of from existing Monte
Carlo results.Comment: 9 pages, 3 figures + Appendices, v2: fixed typos and factors of 2's,
new bound presented in Figure 3, added Appendix
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