Holographic Space-time, Newton's Law and the Dynamics of Black Holes
June 3, 2016
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Physics
High Energy Physics - Theory
We revisit the construction of models of quantum gravity in d dimensional
Minkowski space in terms of random tensor models, and correct some mistakes in
our previous treatment of the subject. We find a large class of models in which
the lar...
Matrix Product Density Operators: Renormalization Fixed Points and
Boundary Theories
June 2, 2016
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Physics
Quantum Physics
Strongly Correlated Electrons
Quantum Physics
Strongly Correlated Electrons
We consider the tensors generating matrix product states and density
operators in a spin chain. For pure states, we revise the renormalization
procedure introduced by F. Verstraete et al. in 2005 and characterize the
tensors corresponding t...
Pfaffian Schur processes and last passage percolation in a half-quadrant
June 1, 2016
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Mathematics
Physics
Probability
Statistical Mechanics
Mathematical Physics
Mathematical Physics
Probability
Statistical Mechanics
Mathematical Physics
Mathematical Physics
We study last passage percolation in a half-quadrant, which we analyze within
the framework of Pfaffian Schur processes. For the model with exponential
weights, we prove that the fluctuations of the last passage time to a point on
the diago...
The real parts of the nontrivial Riemann zeta function zeros
June 1, 2016
Mathematics
General Mathematics
This theorem is based on holomorphy of studied functions and the fact that
near a singularity point the real part of some rational function can take an
arbitrary preassigned value....
Riemann hypothesis equivalences, Robin inequality, Lagarias criterion,
and Riemann hypothesis
May 25, 2016
Mathematics
General Mathematics
In this paper, we briefly review most of accomplished research in Riemann
Zeta function and Riemann hypothesis since Riemann's age including Riemann
hypothesis equivalences as well. We then make use of Robin and Lagarias'
criteria to prove ...
Differential forms on diffeological spaces and diffeological gluing, I
May 24, 2016
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Mathematics
Differential Geometry
Differential Geometry
This paper aims to describe the behavior of diffeological differential forms
under the operation of gluing of diffeological spaces along a smooth map. In
the diffeological context, two ways of looking at diffeological forms are
available, t...
Impact of post-Born lensing on the CMB
May 18, 2016
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Physics
Cosmology and Nongalactic Astrophysics
General Relativity and Quantum Cosmology
Lensing of the CMB is affected by post-Born lensing, producing corrections to
the convergence power spectrum and introducing field rotation. We show
numerically that the lensing convergence power spectrum is affected at the
≲0.2%...
This book is an introductory course to basic commutative algebra with a
particular emphasis on finitely generated projective modules. We adopt the
constructive point of view, with which all existence theorems have an explicit
algorithmic co...
Borel version of the Local Lemma
May 16, 2016
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Mathematics
Probability
Dynamical Systems
Combinatorics
We prove a Borel version of the local lemma, i.e. we show that, under
suitable assumptions, if the set of variables in the local lemma has a
structure of a Borel space, then there exists a satisfying assignment which is
a Borel function. Th...
Some Epistemic Extensions of G\"odel Fuzzy Logic
May 12, 2016
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Mathematics
Logic
In this paper we prove soundness and completeness of some epistemic
extensions of G\"odel fuzzy logic, based on Kripke models in which both
propositions at each state and accessibility relations take values in [0,1]. We
adopt belief as our ...