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The holographic transformation, belief propagation and loop calculus are generalized to problems in generalized probabilistic theories including quantum mechanics. In this work, the partition function of classical factor graph is…
We consider stochastic equations of the form $X_k = \phi_k(X_{k+1}) Z_k$, $k \in \mathbb{N}$, where $X_k$ and $Z_k$ are random variables taking values in a compact group $G_k$, $\phi_k: G_{k+1} \to G_k$ is a continuous homomorphism, and the…
Stochastic quantization is applied to derivation of the equations for the Wilson loops and generating functionals of the Wilson loops in the large-N limit. These equations are treated both in the coordinate and momentum representations. In…
A stochastic calculus is given for processes described by stochastic integrals with respect to fractional Brownian motions and Rosenblatt processes somewhat analogous to the stochastic calculus for It\^{o} processes. These processes for…
We provide a detailed derivation of the Karhunen-Lo\`eve expansion of a stochastic process. We also discuss briefly Gaussian processes, and provide a simple numerical study for the purpose of illustration.
We introduce a fractional generalization of the Erlang Queues $M/E_k/1$. Such process is obtained through a time-change via inverse stable subordinator of the classical queue process. We first exploit the (fractional) Kolmogorov forward…
The characteristic representation, or Goursat problem, for the Klein-Fock-Gordon equation with Volkov interaction [1] is regarded. It is shown that in this representation the explicit form of the Volkov propagator can be obtained. Using the…
In this paper we suggest a simple mathematical procedure to derive the classical probability density of quantum systems via Bohr's correspondence principle. Using Fourier expansions for the classical and quantum distributions, we assume…
This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…
In the large momentum transfer limit, generalized parton distributions can be calculated through a QCD factorization theorem which involves perturbatively-calculable hard kernels and light-cone parton distribution amplitudes of hadrons. We…
In this article, we derive a Stratonovich and Skorohod type change of variables formula for a multidimensional Gaussian process with low H\"older regularity (typically lower than 1/4). To this aim, we combine tools from rough paths theory…
The G-Wishart distribution is an essential component for the Bayesian analysis of Gaussian graphical models as the conjugate prior for the precision matrix. Evaluating the marginal likelihood of such models usually requires computing…
We compute the parton distributions for the chiral quark model. We present a new technique for performing such computations based on Green functions. This approach avoids a discretization of the spectrum. It therefore does not need any…
We prove a Hochschild-Kostant-Rosenberg theorem ("the HKR theorem") which computes the factorization homology of certain smooth commutative ring spectra. In doing so we fix and generalize a THH computation which was first conceived as the…
Fractional Gaussian noise models the time series with long-range dependence; when the Hurst index $H>1/2$, it has positive correlation reflecting a persistent autocorrelation structure. This paper studies the numerical method for solving…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
Aspects of the QCD parton densities are briefly reviewed, drawing some parallels to the density matrix formulation of quantum mechanics, exemplified by Wigner functions. We elaborate on the solution of their evolution equations using…
The discard ZX-calculus is known to be complete and universal for mixed-state quantum mechanics, allowing for both quantum and classical processes. However, if the quantum aspects of ZX-calculus have been explored in depth, little work has…
Long distance contribution to the $K^0-\bar K^0$ mixing is taken into account consistently and the corrections to the naive duality result represented by the famous box diagram are found to be small. Estimates are given in the leading order…
We consider approximating of the median of absolutely continuous distribution given by a probability density function $f$. We assume that $f$ has $r$ continuous derivatives, with derivative of order $r$ being H\"older continuous with the…