相关论文: Grid entropy in a "choose the best of D samples" m…

Working in the setting of i.i.d. last-passage percolation on $\mathbb{R}^D$ with no assumptions on the underlying edge\hyp{}weight distribution, we arrive at the notion of grid entropy - a Subadditive Ergodic Theorem limit of the entropies…

After a brief historical survey, the paper introduces the notion of entropic model sets (cut and project sets), and, more generally, the notion of diffractive point sets with entropy. Such sets may be thought of as generalizations of…

Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…

We study Abelian sandpiles on graphs of the form $G \times I$, where $G$ is an arbitrary finite connected graph, and $I \subset \Z$ is a finite interval. We show that for any fixed $G$ with at least two vertices, the stationary measures…

We applied tensor network contraction algorithms to compute the hard-core lattice gas model, i.e., the enumeration of independent sets on grid graphs. We observed the influence of surface effect and parity effect on the enumeration (and…

In this paper, we study the entropy of a hard random geometric graph (RGG), a commonly used model for spatial networks, where the connectivity is governed by the distances between the nodes. Formally, given a connection range $r$, a hard…

This monograph resolves - in a dense class of cases - several open problems concerning geodesics in i.i.d. first-passage percolation on $\mathbb{Z}^d$. Our primary interest is in the empirical measures of edge-weights observed along…

Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…

Analytic continuation of imaginary time or frequency data to the real axis is a crucial step in extracting dynamical properties from quantum Monte Carlo simulations. The average spectrum method provides an elegant solution by integrating…

Limits of densities belonging to an exponential family appear in many applications, {e.g.} Gibbs models in Statistical Physics, relaxed combinatorial optimization, coding theory, critical likelihood computations, Bayes priors with singular…

For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian…

We study the following question in the context of imitation learning for continuous control: how are the underlying stability properties of an expert policy reflected in the sample-complexity of an imitation learning task? We provide the…

We introduce an exactly solvable lattice model that reveals a universal finite-size scaling law for configurational entropy driven purely by geometry. Using exact enumeration via Burnside's lemma, we compute the entropy for diverse 1D, 2D,…

Consider a statistical physical model on the $d$-regular infinite tree $T_{d}$ described by a set of interactions $\Phi$. Let $\{G_{n}\}$ be a sequence of finite graphs with vertex sets $V_n$ that locally converge to $T_{d}$. From $\Phi$…

Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…

Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from…

We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…

Verifying uniform conditions over continuous spaces through random sampling is fundamental in machine learning and control theory, yet classical coverage analyses often yield conservative bounds, particularly at small failure probabilities.…

Obtaining high certainty in predictive models is crucial for making informed and trustworthy decisions in many scientific and engineering domains. However, extensive experimentation required for model accuracy can be both costly and…

We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The…