arXiv subjects

Masato Hisakado

Publications and source records attributed to Masato Hisakado.

47 records · Page 3Linked to original sources

arXiv2008

Infectious Default Model with Recovery and Continuous Limit

We introduce an infectious default and recovery model for N obligors. Obligors are assumed to be exchangeable and their states are described by N Bernoulli random variables S_{i} (i=1,...,N). They are expressed by multiplying independent Bernoulli variables X_{i},Y_{ij},Y'_{ij}, and default and recovery infections are described by Y_{ij} and Y'_{ij}. We obtain the default probability function P(k) for k defaults. Taking its continuous limit, we find two nontrivial probability distributions with the reflection symmetry of S_{i} \leftrightarrow 1-S_{i}. Their profiles are singular and oscillating and we understand it theoretically. We also compare P(k) with an implied default distribution function inferred from the quotes of iTraxx-CJ. In order to explain the behavior of the implied distribution, the recovery effect may be necessary.

physics.data-an↗

arXiv1998

KPZ Equation and Surface Growth Model

We consider the ultra-discrete Burgers equation. All variables of the equation are discrete. We classify the equation into five regions in the parameter space. We discuss behavior of solutions. Using this equation we construct the deterministic surface growth models respectively. Furthermore we introduce noise into the ultra-discrete Burgers equation. We present the automata models of the KPZ equation. One model corresponds to the discrete version of the ASEP and the other to the Kim-Kosterlitz model.

cond-mat↗

arXiv1998

Hungry Volterra equation, multi boson KP hierarchy and Two Matrix Models

We consider the hungry Volterra hierarchy from the view point of the multi boson KP hierarchy. We construct the hungry Volterra equation as the Bäcklund transformations (BT) which are not the ordinary ones. We call them ``fractional '' BT. We also study the relations between the (discrete time) hungry Volterra equation and two matrix models. From this point of view we study the reduction from (discrete time) 2d Toda lattice to the (discrete time) hungry Volterra equation.

hep-th↗

arXiv1998

The Davey Stewartson system and the Bäcklund Transformations

We consider the (coupled) Davey-Stewartson (DS) system and its Bäcklund transformations (BT). Relations among the DS system, the double Kadomtsev-Petviashvili (KP) system and the Ablowitz-Ladik hierarchy (ALH) are established. The DS hierarchy and the double KP system are equivalent. The ALH is the BT of the DS system in a certain reduction. {From} the BT of coupled DS system we can obtain new coupled derivative nonlinear Schrödinger equations.

solv-int↗

arXiv1997

Chiral solitons from dimensional reduction of Chern-Simons gauged coupled non-linear Schrödinger model

The soliton structure of a gauge theory proposed to describe chiral excitations in the multi-Layer Fractional Quantum Hall Effect is investigated. A new type of derivative multi-component nonlinear Schrödinger equation emerges as effective description of the system that supports novel chiral solitons. We discuss the classical properties of the solutions and study relations to integrable systems.

hep-th↗

arXiv1997

Unitary Matrix Models and Phase Transition

We study the unitary matrix model with a topological term. We call the topological term the theta term. In the symmetric model there is the phase transition between the strong and weak coupling regime at $λ_{c}=2$. If the Wilson term is bigger than the theta term, there is the strong-weak coupling phase transition at the same $λ_{c}$. On the other hand, if the theta term is bigger than the Wilson term, there is only the strong coupling regime. So the topological phase transition disappears in this case.

hep-th↗

arXiv1997

Five-Dimensional Gauge Theories and Whitham-Toda Equation

The five-dimensional supersymmetric SU(N) gauge theory is studied in the framework of the relativistic Toda chain. This equation can be embedded in two-dimensional Toda lattice hierarchy. This system has the conjugate structure. This conjugate structure corresponds to the charge conjugation.

hep-th↗

arXiv1997

Coupled Nonlinear Schrödinger equation and Toda equation (the Root of Integrability)

We consider the relation between the discrete coupled nonlinear Schrödinger equation and Toda equation. Introducing complex times we can show the intergability of the discrete coupled nonlinear Schrödinger equation. In the same way we can show the integrability in coupled case of dark and bright equations. Using this method we obtain several integrable equations.

solv-int↗

arXiv1996

Unitary Matrix Models with a topological term and discrete time Toda equation

We study the full unitary matrix models. Introducing a new term $l log U$, l plays the role of the discrete time. On the other hand, the full unitary matrix model contains a topological term. In the continuous limit it gives rise to a phase transition at $θ=π$. The ground state is characterize by the discrete time l. The discrete time l plays like the instanton number.

hep-th↗

arXiv1996

Unitary Matrix Models and Painlevé III

We discussed the full unitary matrix models from the view points of integrable equations and string equations. Coupling the Toda equations and the string equations, we derive a special case of the Painlevé III equation. From the Virasoro constrains, we can use the radial coordinate. The relation between $t_{1}$ and $t_{-1}$ is like the complex conjugate. %An implicit to the $t\bar{t}$ fusion of topological sigma model %is therby expected.

hep-th↗

arXiv1996

Matrix Models of Two-dimensional Gravity and Discrete Toda Theory

Recursion relations for orthogonal polynominals, arising in the study of the one-matrix model of two-dimensional gravity, are shown to be equvalent to the equations of the Toda-chain hierarchy supplemented by additional Virasoro constraints. This is the case without the double scaling limit. A discrete time variable to the matrix model is introduced. The discrete time dependent partition functions are given by $τ$ functions which satisfy the discrete Toda molecule equation. Further the relations between the matrix model and the discrete time Toda theory are discussed.

hep-th↗