Related papers: Towards a gauge invariant volume-weighted probabil…
We prove existence of (at most denumerable many) absolutely continuous invariant probability measures for random one-dimensional dynamical systems with asymptotic expansion. If the rate of expansion (Lyapunov exponents) is bounded away from…
We comment on recently proposed dissipative inflationary models. It is shown that the strength of the inflationary expansion is related to a specific combination of thermodynamic variables which is known to measure the instability of…
We consider a gauge-invariant Hamiltonian analysis for Yang-Mills theories in three spatial dimensions. The gauge potentials are parametrized in terms of a matrix variable which facilitates the elimination of the gauge degrees of freedom.…
We consider the eternal inflation scenario of the slow-roll/chaotic type with the additional element of an objective collapse of the wave function. The incorporation of this new agent to the traditional inflationary setting might represent…
In \cite{Ch91a} it was shown that the billiard ball map for the periodic Lorentz gas has infinite topological entropy. In this article we study the set of points with infinite Lyapunov exponents. Using the cell structure developed in…
In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of…
We identify a recently proposed shifting operation on classical phase space as a gauge transformation for statistical mechanical microstates. The infinitesimal generators of the continuous gauge group form a non-commutative Lie algebra,…
We make a proposal for gauge-invariant observables in perturbative quantum gravity in cosmological spacetimes, building on the recent work of Brunetti et al. [JHEP 08 (2016) 032]. These observables are relational, and are obtained by…
We give an introductory account of the recently identified gauge invariance of the equilibrium statistical mechanics of classical many-body systems [J. M\"uller et al., Phys. Rev. Lett. Phys. Rev. Lett. 133, 217101 (2024)]. The gauge…
In this paper we investigate extended inflation with an exponential potential $V(\sigma)= V_0 e^{-\kappa\sigma}$, which provides a simple cosmological scenario where the distribution of the constants of Nature is mostly determined by…
A gauge-invariant formulation for the gravitational wave equations is presented. Using this approach, weak, plane wave solutions in a vacuum are derived in various theories. These include general relativity with two modes of polarization…
In this work we analyze the concept of swap-invariance, which is a weaker variant of exchangeability. A random vector $\xi$ in $\mathbb{R}^n$ is called swap-invariant if $\,{\mathbf E}\,\big| \!\sum_j u_j \xi_j \big|\,$ is invariant under…
We study the Benjamin-Ono equation, posed on the torus. We prove that an infinite sequence of weighted gaussian measures, constructed in our previous work, are invariant by the flow of the equation. These measures are supported by Sobolev…
A sufficient geometrical condition for the existence of absolutely continuous invariant probability measures for S-unimodal maps will be discussed. The Lebesgue typical existence of such measures in the quadratic family will be a…
We are interested in Filippov systems which preserve a probability measure on a compact manifold. We define a measure to be invariant for a Filippov system as the natural analogous definition of invariant measure for flows. Our main result…
Present treatments of eternal inflation regulate infinities by imposing a geometric cutoff. We point out that some matter systems reach the cutoff in finite time. This implies a nonzero probability for a novel type of catastrophe. According…
In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…
The quantum behavior of noncommutative eternal inflation is quite different from the usual knowledge. Unlike the usual eternal inflation, the quantum fluctuation of noncommutative eternal inflation is suppressed by the Hubble parameter. Due…
In this work, we identify the most general measure of arbitrage for any market model governed by It\^o processes. We show that our arbitrage measure is invariant under changes of num\'{e}raire and equivalent probability. Moreover, such…
In this paper, we give a possible solution to the cosmological constant problem. It is shown hat the traditional approach, based on volume weighting of probabilities, leads to an incoherent onclusion: the probability that a randomly chosen…