Related papers: Master equation for the finite state space plannin…
The steady states of the master equation are investigated. We give two expressions for the steady state distribution of the master equation a la the Zubarev-McLennan steady state distribution, i.e., the exact expression and an expression…
In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the…
We study the convergence problem of mean-field control theory in the presence of state constraints and non-degenerate idiosyncratic noise. Our main result is the convergence of the value functions associated to stochastic control problems…
Motivated by a phenomenon of phase transition in a model of alignment of self-propelled particles, we obtain a kinetic mean-field equation which is nothing else than the Doi equation (also called Smoluchowski equation) with dipolar…
We present coincidence and common fixed point results of selfmappings satisfying a contraction type in partially ordered metric spaces. As an application, we give an existence theorem for a common solution of integral equations.
This paper investigates the well-posedness of a type of state constraint ergodic Mean Field Game system in a bounded domain in which the Hamilton-Jacobi-Bellman equation is paired with an infinite Dirichlet boundary condition. In this…
A quantum master equation is obtained for identical fermions by including a relaxation term in addition to the mean-field Hamiltonian. [Huang C F and Huang K N 2004 Chinese J. Phys. ${\bf 42}$ 221; Gebauer R and Car R 2004 Phys. Rev. B…
This chapter examines monotonicity techniques in the theory of mean-field games(MFGs). Originally, monotonicity ideas were used to establish the uniqueness of solutions for MFGs. Later, monotonicity methods and monotone operators were…
The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance, and sociodynamics. We consider the master equation with periodic transition rates. This may represent an…
From the field equations in the linear regime of the characteristic formulation of general relativity, Bishop, for a Schwarzschild's background, and M\"adler, for a Minkowski's background, were able to show that it is possible to derive a…
We put forth a new class of quantum master equations that correctly reproduce the asymptotic state of an open quantum system beyond the infinitesimally weak system-bath coupling limit. Our method is based on incorporating the knowledge of…
In this paper, we prove uniqueness of solutions of mean field equations with general boundary conditions for the critical and subcritical total mass regime, extending the earlier results for null Dirichlet boundary condition. The proof is…
We consider a unique continuation problem for the wave equation given data in a volumetric subset of the space time domain. In the absence of data on the lateral boundary of the space-time cylinder we prove that the solution can be…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
We consider solutions satisfying the Neumann zero boundary condition and a linearized mean field game system in $\Omega \times (0,T)$, where $\Omega$ is a bounded domain in $\mathbb{R}^d$ and $(0,T)$ is the time interval. We prove two kinds…
We investigate a first-order mean field planning problem of the form \begin{equation} \left\lbrace\begin{aligned} -\partial_t u + H(x,Du) &= f(x,m) &&\text{in } (0,T)\times \mathbb{R}^d, \\ \partial_t m - \nabla\cdot (m\,H_p(x,Du)) &= 0…
This paper analyzes the convergence of the finite population optimal stopping problem towards the corresponding mean field limit. Building on the viscosity solution characterization of the mean field optimal stopping problem of our previous…
We present here the linear regime of the Einstein's field equations in the characteristic formulation. Through a simple decomposition of the metric variables in spin-weighted spherical harmonics, the field equations are expressed as a…
The basic concepts of non-commutative probability theory are reviewed and applied to the large $N$ limit of matrix models. We argue that this is the appropriate framework for constructing the master field in terms of which large $N$…
Our recent interest is focused on establishing the necessary and sufficient conditions that guarantee a long-term stable evolution of both natural and artificial systems. Two necessary conditions, called global and local boundedness, are…