Related papers: A variational principle for a non-integrable model
We study the well-known variational and large deviation principle for graph homomorphisms from $\mathbb{Z}^m$ to $\mathbb{Z}$. We provide a robust method to deduce those principles under minimal a priori assumptions. The only ingredient…
We consider homogenization of random surfaces and study the variational principle for graph homomorphisms from subsets of $\mathbb{Z}^m$ into $\mathbb{Z}$, where the underlying uniform measure is perturbed by a random field. Motivated by…
We provide an existence theory for gradient Gibbs measures for Z-valued spin models on regular trees which are not invariant under translations of the tree, assuming only summability of the transfer operator. The gradient states we obtain…
A variation principle for mass transport in solids is derived that recasts transport coefficients as minima of local thermodynamic average quantities. The result is independent of diffusion mechanism, and applies to amorphous and…
We consider a discrete-time dynamical process on graphs, firstly introduced in connection with a protocol for controlling large networks of spin 1/2 quantum mechanical particles [Phys. Rev. Lett. 99, 100501 (2007)]. A description is as…
The present article studies variational principles for the formulation of static and dynamic problems involving Kirchhoff rods in a fully nonlinear setting. These results, some of them new, others scattered in the literature, are presented…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
We study Gibbsian models of unbounded integer-valued spins on trees which possess a symmetry under height-shift. We develop a theory relating boundary laws to gradient Gibbs measures, which applies also in cases where the corresponding…
Extremal graphical models are sparse statistical models for multivariate extreme events. The underlying graph encodes conditional independencies and enables a visual interpretation of the complex extremal dependence structure. For the…
We study thermodynamical formalism of a discrete nonautonomous dynamical system determined by a sequence of continuous self-maps of a compact metric space. Using the methods of Convex Analysis we get variational principles for pressure…
For random dynamical systems, by summarizing the fundamental properties of Kifer's topological pressure we introduce the concept of random pressure functions, and define Ruelle's metric entropy for invariant measures. Employing the…
We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix…
Out-of-distribution generalization under distributional shifts remains a critical challenge for graph neural networks. Existing methods generally adopt the Invariant Risk Minimization (IRM) framework, requiring costly environment…
A covariance graph is an undirected graph associated with a multivariate probability distribution of a given random vector where each vertex represents each of the different components of the random vector and where the absence of an edge…
We define a range of new coarse geometric invariants based on various graph-theoretic measures of complexity for finite graphs, including: treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these…
Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for…
We consider a Random Graph Model on $\mathbb{Z}^{d}$ that incorporates the interplay between the statistics of the graph and the underlying space where the vertices are located. Based on a graphical construction of the model as the…
In the recent years, with the incorporation of contact geometry, there has been a renewed interest in the study of dissipative or non-conservative systems in physics and other areas of applied mathematics. The equations arising when…
In this work, we consider an extension of graphical models to random graphs, trees, and other objects. To do this, many fundamental concepts for multivariate random variables (e.g., marginal variables, Gibbs distribution, Markov properties)…
By employing the differential structure recently developed by N. Gigli, we first give a notion of functions of bounded variation ($BV$) in terms of suitable vector fields on a complete and separable metric measure space $(\mathbb{X},d,\mu)$…