Related papers: Wasserstein Distance in Cosmological Structure For…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
We construct a geometric framework for cosmological large-scale structure based on optimal transport theory and Wasserstein geometry. In this framework, Ricci curvature on the probability measure space $\mathcal{P}_2(M)$ is characterized by…
In this work we test Wasserstein distance in conjunction with persistent homology, as a tool for discriminating large scale structures of simulated universes with different values of $\sigma_8$ cosmological parameter (present…
An attractive and simple hypothesis for the formation of large-scale structure is that it developed by gravitational instability from primordial fluctuations with an initially Gaussian probability distribution. Non-linear gravitational…
The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal…
We develop a measure-theoretic framework for galaxy evolution in which galaxy populations are described as probability measures on a state space. Galaxy evolution is represented as the time evolution of a measure $\nu_t$, governed by the…
The sliced-Wasserstein flow is an evolution equation where a probability density evolves in time, advected by a velocity field computed as the average among directions in the unit sphere of the optimal transport displacements from its 1D…
Models of structure formation in the universe postulate that matter distributions observed today in galaxy catalogs arise, through a complex non-linear dynamics, by gravitational evolution from a very uniform initial state. Dark matter…
I review the standard paradigm for understanding the formation and evolution of cosmic structure, based on the gravitational instability of dark matter, but many variations on this basic theme are viable. Despite the great progress that has…
Thermodynamics serves as a universal means for studying physical systems from an energy perspective. In recent years, with the establishment of the field of stochastic and quantum thermodynamics, the ideas of thermodynamics have been…
This paper reviews selected aspects of the growth of cosmological structure, covering the following general areas: (1) expected characteristics of linear density perturbations according to various candidate theories for the origin of…
Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
Optimal transport and Wasserstein distance are prominent tools to quantify the space of probability distributions. From a novel viewpoint of manifold hypothesis in machine learning being a possible guide for the holographic principle, we…
This article reviews the prevailing paradigm for how galaxies and larger structures formed in the universe: gravitational instability. Basic observational facts are summarized to motivate the standard cosmological framework underlying most…
I outline the connections between some of the most widely used statistical measures of galaxy clustering and the fundamental issues in the theory of structure formation. I devote particular attention to the problem of biasing, i.e. to a…
We study the problem of quantifying how far an empirical distribution deviates from Gaussianity under the framework of optimal transport. By exploiting the cone geometry of the relative translation invariant quadratic Wasserstein space, we…
We discuss correlation properties of a general mass density field introducing a classification of structures based on their complexity. Standard cosmological models for primordial mass fluctuations are characterized by a sort of large-scale…
The currently standard theory of cosmic structure formation posits that the present-day clumpy appearance of the universe developed through gravitational amplification of the matter density fluctuations that are generated in the very early…
Cosmic structures at large scales represent the earliest and most extended form of matter condensation. In this lecture we review the application of the methods and concepts of modern statistical physics to these structures. This leads to a…
The cosmic large scale structure encodes the formation and evolution of a weblike network of dark matter and galaxies within the Universe. The cosmological information is wrapped up in non-Gaussian statistics requiring characterisation…