arXiv subjects

Oliver Baker

Publications and source records attributed to Oliver Baker.

4 recordsLinked to original sources

arXiv2026

Entropy and Distributed Source Coding of Connected Soft Random Geometric Graphs

We consider the distributed compression of Soft Random Geometric Graphs (SRGGs) above the connectivity threshold. We establish the Slepian-Wolf rate region for the SRGG in the setting where there are a finite number of encoders compressing sections of the graph independently. To do so, we prove novel limit theorems and asymptotic equipartition properties for the SRGG and its entropy, which allow us to use random binning techniques for distributed compression.

cs.IT↗

arXiv2026

Entropy of Soft Random Geometric Graphs in General Geometries

We study the effect of the choice of embedding geometry on the entropy of random geometric graph ensembles with soft connection functions. First we show that when the connection range is small, the entropy is dependent only on the dimension of the geometry and not the shape, but for large connection ranges the boundaries of the domain matter. Next, we formulate the problem of estimating entropy as a problem of estimating the average degree of a graph with the binary entropy function as its connection function. We use this formulation to study the effect of boundaries on the entropy, and to estimate the entropy of soft random geometric graphs in complicated geometries where a closed form pair distance density is not available.

math.PR↗

arXiv2025

Entropy of Random Geometric Graphs in High and Low Dimensions

We use a multivariate central limit theorem (CLT) to study the distribution of random geometric graphs (RGGs) on the cube and torus in the high-dimensional limit with general node distributions. We find that the distribution of RGGs on the torus converges to the Erd\H os-R\'enyi (ER) ensemble when the nodes are uniformly distributed, but that the distribution for RGGs with non-uniformly distributed nodes on the torus, and for RGGs with any distribution of nodes with kurtosis greater than 1 on the cube is different. In these cases, the distribution has a lower maximum entropy than the ER ensemble, but is still symmetric. Soft RGGs in either geometry converge to the ER ensemble. An Edgeworth correction to the CLT is then developed to derive the $\mathcal{O}\left(d^{-\frac{1}{2}}\right)$ sub-leading term of the Shannon entropy of RGGs in dimension for both geometries. We also provide numerical approximations of maximum entropy in low-dimensional hard and soft RGGs, and calculate exactly the entropy of hard RGGs with 3 nodes in the one-dimensional cube and torus.

math.PR↗

arXiv2024

Investigating the Role of Quantum Entanglement in Heavy Ion Collisions through Elliptic Flow

This paper investigates the relationship between initial spatial anisotropy and final state momentum anisotropy in heavy ion collisions through the analysis of elliptic flow ($v_2$) as a function of transverse momentum ($p_T$). Building upon previous studies on thermalization in heavy ion collisions using transverse momentum distributions, we extend the analysis to the $p_T$ dependence of $v_2$ in Pb-Pb and Xe-Xe collisions. By employing a two-component model to extract the thermal and hard scattering contributions to the elliptic flow, we aim to gain further insights into the role of quantum entanglement in the rapid thermalization and collective behavior of the quark-gluon plasma (QGP).

nucl-th↗