Related papers: Beyond Complex Langevin Equations: positive repres…
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.
Let a ``complex probability'' be a normalizable complex distribution $P(x)$ defined on $\R^D$. A real and positive probability distribution $p(z)$, defined on the complex plane $\C^D$, is said to be a positive representation of $P(x)$ if…
Recent work has addressed the problem of inferring Langevin dynamics from data. In this work, we address the problem of relating terms in the Langevin equation to statistical properties, such as moments of the probability density function…
A simple construction of Euclidean invariant and reflection positive measures on the cylindrical compactification is performed under a weaker hypothesis than has recently been obtained. Moreover, the results are extended to the case when…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
On the basis of general considerations, we propose a Langevin equation accounting for critical phenomena occurring in the presence of two symmetric absorbing states. We study its phase diagram by mean-field arguments and direct numerical…
We explicitly construct the structure of Jacquet modules of parabolically induced representations of even unitary groups and even general unitary groups over a $p$-adic field $F$ of characteristic different than two. As an application, we…
We describe a generalization of the large sieve to situations where the underlying groups are nonabelian, and give several applications to the arithmetic of abelian varieties. In our applications, we sieve the set of primes via the system…
Enlarging on Parts I, II, and III we write more equations in the desired format of the extended abstract theory of composites. We focus on a multitude of equations involving higher order derivatives. The motivation is that results and…
The aim of this note is to point out a convexity property with respect to the root lattice for the support of the highest weights that occur in a tensor product of irreducible rational representations of $SL(n)$ over the complex numbers.…
The ability to describe strongly interacting matter at finite temperature and baryon density provides the means to determine, for instance, the equation of state of QCD at non-zero baryon chemical potential. From a theoretical point of…
A simple construction is given of a class of Euclidean invariant, reflection positive measures on a compactification of the space of distributions. An unusual feature is that the regularizations used are not reflection positive.
A model of representations of a Lie algebra is a representation which a direct sum of all irreducible finite dimensional representations taken with multiplicity $1$. In the paper an explicit construction of a model of representation for all…
I review the presence of the sign problem in lattice QCD at nonzero baryon density and its relation with the overlap and Silver Blaze problems. I then discuss progress in some cases where the sign problem can be handled, either because the…
We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…
Recent progress of the complex Langevin method and the Lefschetz thimble in connection with the sign problem is reviewed. These methods rely on the complexification of the original field manifold and they allow direct simulations of…
Dual formulations of Abelian U(1) and Z(N) LGT with a static fermion determinant are constructed at finite temperatures and non-zero chemical potential. The dual form is valid for a broad class of lattice gauge actions, for arbitrary number…
Stationary distributions of complex Langevin equations are shown to be the complexified path integral solutions of the Schwinger-Dyson equations of the associated quantum field theory. Specific examples in zero dimensions and on a lattice…
Let $T$ be a positive closed current of unit mass on the complex projective space $\mathbb P^n$. For certain values $\alpha<1$, we prove geometric properties of the set of points in $\mathbb P^n$ where the Lelong number of $T$ exceeds…
We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann's theorem to the complex case by proving that complex…