Zobrazeno 1 - 10
of 669
pro vyhledávání: '"Hirsch Christian"'
Autor:
Hirsch, Christian, Petráková, Martina
In this paper, we present a large deviation theory developed for functionals of canonical Gibbs processes, i.e., Gibbs processes with respect to the binomial point process. We study the regime of a fixed intensity in a sequence of increasing windows.
Externí odkaz:
http://arxiv.org/abs/2411.18483
We consider Betti numbers of the excursion of a smooth Euclidean Gaussian field restricted to a rectangular window, in the asymptotics where the window grows to R^d . With motivations coming from Topological Data Analysis, we derive a functional Cent
Externí odkaz:
http://arxiv.org/abs/2411.11429
Autor:
Hirsch, Christian, Owada, Takashi
This paper considers limit theorems associated with subgraph counts in the age-dependent random connection model. First, we identify regimes where the count of sub-trees converges weakly to a stable random variable under suitable assumptions on the s
Externí odkaz:
http://arxiv.org/abs/2409.05226
In this paper, we introduce a novel model for random hypergraphs based on weighted random connection models. In accordance with the standard theory for hypergraphs, this model is constructed from a bipartite graph. In our stochastic model, both verte
Externí odkaz:
http://arxiv.org/abs/2407.16334
We investigate the percolation properties of a planar reinforced network model. In this model, at every time step, every vertex chooses $k \ge 1$ incident edges, whose weight is then increased by 1. The choice of this $k$-tuple occurs proportionally
Externí odkaz:
http://arxiv.org/abs/2407.12484
Autor:
Hirsch, Christian, Willhalm, Daniel
We study large deviations in the context of stochastic gradient descent for one-hidden-layer neural networks with quadratic loss. We derive a quenched large deviation principle, where we condition on an initial weight measure, and an annealed large d
Externí odkaz:
http://arxiv.org/abs/2403.09310
We present a process-level Poisson-approximation result for the degree-k vertices in a high-density weighted random connection model with preferential-attachment kernel in the unit volume. Our main focus lies on the impact of the left tails of the we
Externí odkaz:
http://arxiv.org/abs/2311.12643
In this paper, we derive cumulant bounds for subgraph counts and power-weighted edge length in a class of spatial random networks known as weighted random connection models. This involves dealing with long-range spatial correlations induced by the pr
Externí odkaz:
http://arxiv.org/abs/2311.00600
Autor:
Hirsch, Christian, Nam, Kyeongsik
Isoperimetric profile describes the minimal boundary size of a set with a prescribed volume. Itai Benjamini conjectured that the isoperimetric profile of the giant component in supercritical percolation experiences an averaging effect and satisfies t
Externí odkaz:
http://arxiv.org/abs/2309.14882
Autor:
Hirsch, Christian, Juhasz, Peter
In this paper, we investigate the potential of the age-dependent random connection model (ADRCM) with the aim of representing higher-order networks. A key contribution of our work are probabilistic limit results in large domains. More precisely, we f
Externí odkaz:
http://arxiv.org/abs/2309.11407