Related papers: From constrained stochastic processes to the nonli…
We develop a new paradigm for finding bifurcations of solutions of nonlinear problems, which is based on the detection of extreme values of new type of variational functional associated with the considering problem. The variational…
The quantum field theory describing the massive O(2) nonlinear sigma-model is investigated through two non-perturbative constructions: The form factor bootstrap based on integrability and the lattice formulation as the XY model. The…
To mimic the complex transport-like collective phenomena in a man-made or natural system, we study an open network junction model of totally asymmetric simple exclusion process with bulk particle attachment and detachment. The stationary…
Recently, the complete left tail asymptotic for the density of the {\it martingale limit} of the classical Galton-Watson process has been derived. The derivation is based on the properties of a special function (whose inverse Fourier…
The O(n) non-linear $\sigma$-model is simulated on 2-dimensional regular and random lattices. We use two different levels of randomness in the construction of the random lattices and give a detailed explanation of the geometry of such…
We explore the perspectives of machine learning techniques in the context of quantum field theories. In particular, we discuss two-dimensional complex scalar field theory at nonzero temperature and chemical potential -- a theory with a…
Diffusion generative models have recently been applied to domains where the available data can be seen as a discretization of an underlying function, such as audio signals or time series. However, these models operate directly on the…
The asymptotic expansion of $n$-dimensional cyclic integrals was expressed as a series of functionals acting on the symmetric function involved in the cyclic integral. In this article, we give an explicit formula for the action of these…
The most general exclusion single species reaction-diffusion models with nearest-neighbor interactions one a one dimensional lattice are investigated, for which the evolution of full intervals are closed. Using a generating function method,…
Open effective field theories provide a systematic framework for describing physical systems interacting with an environment whose microscopic details are unknown, unobservable, or uncalculable. A basic step in constructing any effective…
We investigate a simple generative model for network formation. The model is designed to describe the growth of networks of kinship, trading, corporate alliances, or autocatalytic chemical reactions, where feedback is an essential element…
We study the near-equilibrium critical dynamics of the $O(3)$ nonlinear sigma model describing isotropic antiferromagnets with non-conserved order parameter reversibly coupled to the conserved total magnetization. To calculate response and…
A new functional is presented for variational mesh generation and adaptation. It is formulated based on combining the equidistribution and alignment conditions into a single condition with only one dimensionless parameter. The functional is…
Quantum 3D R-matrix in the classical (i.e. functional) limit gives a symplectic map of dynamical variables. The corresponding 3D evolution model is considered. An auxiliary problem for it is a system of linear equations playing the role of…
We study the problem of the rigorous derivation of one-dimensional models for a thin curved beam starting from three-dimensional nonlinear elasticity. We describe the limiting models obtained for different scalings of the energy. In…
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This…
We study the stochastic quantization of two-dimensional nonlinear sigma model in the large $N$ limit. Our main tool is the {\it effective} Langevin equation with which we investigate nonperturbative phenomena and derive the results which…
The random current representation of the Ising model, along with a related path expansion, has been a source of insight on the stochastic geometric underpinning of the ferromagnetic model's phase structure and critical behavior in different…
In this manuscript, we consider the problem of learning a flow or diffusion-based generative model parametrized by a two-layer auto-encoder, trained with online stochastic gradient descent, on a high-dimensional target density with an…
We show that the action of a dynamical system can be supplemented by an effective action for its environment to reproduce arbitrary coordinate dependent ohmic dissipation and gyroscopic forces. The action is a generalization of the harmonic…