相关论文: The Statistics of the Points Where Nodal Lines Int…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…
We study the statistical distribution of the closest encounter between generic smooth observations computed along different trajectories of a rapidly mixing dynamical system. At the limit of large trajectories, we obtain a distribution of…
Stochastic network influences complicate graph filter design by producing uncertainty in network iteration matrix eigenvalues, the points at which the graph filter response is defined. While joint statistics for the eigenvalues typically…
We introduce a set of iterative equations that exactly solves the size distribution of components on small arbitrary graphs after the random removal of edges. We also demonstrate how these equations can be used to predict the distribution…
We introduce a random intersection graph process aimed at modeling sparse evolving affiliation networks that admit tunable (power law) degree distribution and assortativity and clustering coefficients. We show the asymptotic degree…
We investigate the large deviation behaviour of a point process sequence based on a stationary symmetric stable non-Gaussian discrete-parameter random field using the framework of Hult and Samorodnitsky (2010). Depending on the ergodic…
We study the low-energy physics of the critical (2+1)-dimensional random transverse-field Ising model. The one-dimensional version of the model is a paradigmatic example of a system governed by an infinite-randomness fixed point, for which…
Interactions of inhibitory neurons produce gamma oscillations (30--80 Hz) in the local field potential, which is known to be involved in functions such as cognition and attention. In this study, the modified theta model is considered to…
Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…
We consider the uniform random $d$-regular graph on $N$ vertices, with $d \in [N^\alpha, N^{2/3-\alpha}]$ for arbitrary $\alpha > 0$. We prove that in the bulk of the spectrum the local eigenvalue correlation functions and the distribution…
A scalar theory can have many Gaussian (free) fixed points, corresponding to Lagrangians of the form $\phi\,\Box^k\phi$. We use the non-perturbative RG to study examples of flows between such fixed points. We show that the anomalous…
We present a new method for learning Soft Random Geometric Graphs (SRGGs), drawn in probabilistic metric spaces, with the connection function of the graph defined as the marginal posterior probability of an edge random variable, given the…
We have measured the local and global statistics of singularity velocity, v, and have related these through the spatial correlation function of v. The distribution of v is a mixture of a mesoscopic distribution of global change in the…
This article contains a generalization of the authors' results on numbers of nodal points of eigenfunctions on "good curves" in analytic plane domains (arXiv:0710.0101). The term `good' means that the $L^2$ norms of restrictions of…
The magnitude of Pearson correlation between two scalar random variables can be visually judged from the two-dimensional scatter plot of an independent and identically distributed sample drawn from the joint distribution of the two…
We introduce and analyze a class of growing geometric random graphs that are invariant under rescaling of space and time. Directed connections between nodes are drawn according to influence zones that depend on node position in space and…
We compare level-set percolation for Gaussian free fields (GFFs) defined on a rectangular subset of $\delta \mathbb{Z}^2$ to level-set percolation for GFFs defined on the corresponding metric graph as the mesh size $\delta$ goes to 0. In…
Chi-squared random fields arise naturally from the study of fluctuations in field theories with SO(n) symmetry. The extrema of chi-squared fields are of particular physical interest. In this paper, we undertake a statistical analysis of the…
We consider the two-point correlation function of the photodissociation cross section in molecules where the fragmentation process is indirect, passing through resonances above the dissociation threshold. In the limit of overlapping…