相关论文: Tropical variants of some complex analysis results
We first develop the local theory of functions on $\mathbb R^n$ defined by tropical Laurent polynomials. We study the structure of the semiring of functions, where two functions are identified when they coincide on a neighborhood of a fixed…
We consider the effective resummation of a Borel sum by its associated factorial series expansion. Our approach provides concrete estimates for the remainder term when truncating this factorial series. We then generalize a theorem of…
Tropical varieties capture combinatorial information about how coordinates of points in a classical variety approach zero or infinity. We present algorithms for computing the rays of a complex and real tropical curve defined by polynomials…
We study the utility of a complex Langevin (CL) equation as an alternative for the Monte Carlo (MC) procedure in the evaluation of expectation values occurring in fermionic many-body problems. We find that a CL approach is natural in cases…
In this paper, we apply high level versions of Jacobi's derivative formula to number theory such as quarternary quadratic forms and convolution sums of some arithmetical functions.
Starting from certain rational varieties blown-up from (P^1)^N, we construct a tropical, i.e., subtraction-free birational, representation of Weyl groups as a group of pseudo isomorphisms of the varieties. Furthermore, we develop an…
We prove general Cramer type theorems for linear systems over various extensions of the tropical semiring, in which tropical numbers are enriched with an information of multiplicity, sign, or argument. We obtain existence or uniqueness…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
We introduce a sheaf-theoretic approach to tropical homology, especially for tropical homology with potentially non-compact supports. Our setup is suited to study the functorial properties of tropical homology, and we show that it behaves…
We explain how to tropicalize scalar quantum field theory and show that tropicalized massive scalar quantum field theory is exactly solvable. This exact solution manifests as a non-linear recursion equation fulfilled by the expansion…
Let $A$ be an abelian variety over an algebraically closed field $k$ that is complete with respect to a nontrivial nonarchimedean absolute value. Let $A^{\mathrm{an}}$ denote the analytification of $A$ in the sense of Berkovich, and let…
We design a theoretic tree-based functional representation of a class of Feynman-Kac particle distributions, including an extension of the Wick product formula to interacting particle systems. These weak expansions rely on an original…
We apply ideas from intersection theory on toric varieties to tropical intersection theory. We introduce mixed Minkowski weights on toric varieties which interpolate between equivariant and ordinary Chow cohomology classes on complete toric…
We develop a recursive method for perturbative solutions of the Fokker-Planck equation with nonlinear drift. The series expansion of the time-dependent probability density in terms of powers of the coupling constant is obtained by solving a…
In this paper, we study holomorphic curves satisfying the Fubini-Study derivative $\|f'(z)\|=O(|z|^\sigma)$ for some $\sigma>-1$ from the viewpoint of Nevanlinna theory
A new hidden variable theory is proposed, according to which particles follows definite trajectories, as in Bohmian Mechanics or Nelson's stochastic mechanics; in the new theory, however, the trajectories are classical, i.e. Newtonian. This…
Tropical geometry is used to develop a new approach to the theory of discriminants and resultants in the sense of Gel'fand, Kapranov and Zelevinsky. The tropical A-discriminant, which is the tropicalization of the dual variety of the…
This is the first part of the review article which focuses on theory and applications of Herglotz-Nevanlinna functions in material sciences. It starts with the definition of scalar valued Herglotz-Nevanlinna functions and explains in detail…
In this paper, using Nevanlinna's value distribution theory of meromorphic functions in several complex variables, we study for the existence of entire solutions $f$ in $\mathbb{C}^2$ of the following partial differential equation…
Elements of the tropical vertex group, introduced by Kontsevich and Soibelman, are formal families of symplectomorphisms of the 2-dimensional algebraic torus. We prove ordered product factorizations in the tropical vertex group are…