Beyond Complex Langevin Equations: positive representation of a class of complex measures

Complex Langevin Equations and Schwinger-Dyson Equations

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 are given. Relevance to the study of quantum field theory phase space is discussed.

On the irreducibility of the complex specialization of the representation of the Hecke algebra of the complex reflection group $G_7$

We consider a 2-dimensional representation of the Hecke algebra $H(G_7, u)$, where $G_7$ is the complex reflection group and $u$ is the set of indeterminates $u = (x_1,x_2,y_1,y_2,y_3,z_1,z_2,z_3)$. After specializing the indetrminates to non zero complex numbers, we then determine a necessary and sufficient condition that guarantees the irreducibility of the complex specialization of the repre...

Existence of positive solution to a class of boundary value problems of fractional differential equations

This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...

Theory of Hybrid Fractional Differential Equations with Complex Order

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...

Theory of KM2O-Langevin Equations, Complex Phenomena Described by Equations, and Stochastic Analysis of Mathematical Phenomena