Related papers: From the discrete to the continuous - towards a cy…
In quantum gravity, we envision renormalization as the key tool for bridging the gap between microscopic models and observable scales. For spin foam quantum gravity, which is defined on a discretisation akin to lattice gauge theories, the…
A new procedure for coarse-graining dynamical triangulations is presented. The procedure provides a meaning for the relevant value of observables when "probing at large scales", e.g. the average scalar curvature. The scheme may also be…
A first step towards implementing a notion of coarse graining in an intrinsically Lorentzian, discrete quantum- gravity approach, namely causal set quantum gravity is taken. It makes use of an abstract notion of scale, based on counting the…
Spin foams are models of quantum gravity and therefore quantum space time. A key open issue is to determine the possible continuum phases of these models. Progress on this issue has been prohibited by the complexity of the full…
Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and…
Structure-based coarse graining of molecular systems offers a systematic route to reproduce the many-body potential of mean force. Unfortunately, common strategies are inherently limited by the molecular mechanics force field employed.…
A background-independent route towards a universal continuum limit in discrete models of quantum gravity proceeds through a background-independent form of coarse graining. This review provides a pedagogical introduction to the conceptual…
The continuum limit of loop quantum gravity is still an open problem. Indeed, no proper dynamics in known to start with and we still lack the mathematical tools to study its would-be continuum limit. In the present PhD dissertation, we will…
We apply the ``consistent discretization'' approach to general relativity leaving the spatial slices continuous. The resulting theory is free of the diffeomorphism and Hamiltonian constraints, but one can impose the diffeomorphism…
We undertake first steps in making a class of discrete models of quantum gravity, spin foams, accessible to a large scale analysis by numerical and computational methods. In particular, we apply Migdal-Kadanoff and Tensor Network…
An expression for the stress tensor near an external boundary of a discrete mechanical system is derived explicitly in terms of the constituents' degrees of freedom and interaction forces. Starting point is the exact and general coarse…
Coarse graining enables the investigation of molecular dynamics for larger systems and at longer timescales than is possible at atomic resolution. However, a coarse graining model must be formulated such that the conclusions we draw from it…
The Renormalization Group encodes three concepts that could be key to accelerate progress in quantum gravity. First, it provides a micro-macro connection that could connect microscopic spacetime physics to phenomenology at observationally…
We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a…
Discretizations of continuum theories often do not preserve the gauge symmetry content. This occurs in particular for diffeomorphism symmetry in general relativity, which leads to severe difficulties both in canonical and covariant…
High-dimensional recordings of dynamical processes are often characterized by a much smaller set of effective variables, evolving on low-dimensional manifolds. Identifying these latent dynamics requires solving two intertwined problems:…
In this brief article I show how the notion of coarse graining and the Renormalization Group enter naturally in the dynamics of genetic systems, in particular in the presence of recombination. I show how the latter induces a dynamics…
We present the conceptual and technical background required to describe and understand the correlations and fluctuations of the empirical density and current of steady-state diffusion processes on all time scales -- observables central to…
The origin of the phenomenological deterministic laws that approximately govern the quasiclassical domain of familiar experience is considered in the context of the quantum mechanics of closed systems such as the universe as a whole. We…
We consider here a fully discrete variant of the implicit variational scheme for mean curvature flow [AlmTayWan,LucStu], in a setting where the flow is governed by a crystalline surface tension defined by the limit of pairwise interactions…