Related papers: Beyond canonical decoupling
The double scaling limit of a new class of the multi-matrix models proposed in \cite{MMM91}, which possess the $W$-symmetry at the discrete level, is investigated in details. These models are demonstrated to fall into the same universality…
A superposition of a matrix ensemble refers to the ensemble constructed from two independent copies of the original, while a decimation refers to the formation of a new ensemble by observing only every second eigenvalue. In the cases of the…
This paper deals with the Landesman-Lazer type problem of elliptic equations associated with homogeneous Dirichlet boundary conditions. By using some dynamical arguments we derive some new results on bifurcation from infinity and…
Classical finite association schemes lead to a finite-dimensional algebras which are generated by finitely many stochastic matrices. Moreover, there exist associated finite hypergroups. The notion of classical discrete association schemes…
We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their…
We develop a rigidity theory for frameworks in $\mathbb{R}^3$ which have two coincident points but are otherwise generic and only infinitesimal motions which are tangential to a family of cylinders induced by the realisation are considered.…
While any infimum in a poset can also be computed as a supremum, and vice versa, categorical limits and colimits do not always approximate each other. If I approach a point from below, and you approach it from above, then we will surely…
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
We present a method to derive separability criteria for the different classes of multiparticle entanglement, especially genuine multiparticle entanglement. The resulting criteria are necessary and sufficient for certain families of states.…
We study a general class of percolation models in Euclidean space including long-range percolation, scale-free percolation, the weight-dependent random connection model and several other previously investigated models. Our focus is on the…
In the paper, there are new found methods to determine the range of every exceptional element in exceptional set, we can solve Twin primes problem and Goldbach Conjecture problem basically.
We prove sharp $\ell^q L^p$ decoupling inequalities for $p,q \in [2,\infty)$ and arbitrary tuples of quadratic forms. Connections to prior results on decoupling inequalities for quadratic forms are also explained. We also include some…
Specification of the strongest possible Bell inequalities for arbitrarily complicated physical scenarios -- any number of observers choosing between any number of observables with any number of possible outcomes -- is currently an open…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
We discuss the possibility of making the {\it initial} definitions of mutually different (possibly interacting, or even entangled) systems in the context of decoherence theory. We point out relativity of the concept of elementary physical…
Both complete decoupling and tangent decoupling are classical tools aiming to compare two random processes where one has a weaker dependence structure. We give a new proof for the complete decoupling inequality, which provides a lower bound…
Sampling algorithms, hypergraph degree sequences, and polytopes play a crucial role in statistical analysis of network data. This article offers a brief overview of open problems in this area of discrete mathematics from the point of view…
Coupling dark energy to dark matter provides one of the simplest way to effectively modify gravity at large scales without strong constraints from local (i.e. solar system) observations. Models of coupled dark energy have been studied…
Separation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be expressed and studied. This paper offers some basic theory…
We study the set of lines that meet a fixed line and are tangent to two spheres and classify the configurations consisting of a single line and three spheres for which there are infinitely many lines tangent to the three spheres that also…