Small noise spectral gap asymptotics for a large system of nonlinear diffusions

A delay-dependent robust fuzzy control approach is developed for a class of nonlinear uncertain interconnected time delay large systems in this paper. First, an equivalent T–S fuzzy model is extended in order to accurately represent nonlinear dynamics of the large system. Then, a decentralized state feedback robust controller is proposed to guarantee system stabilization with a prescribedH∞disturbance attenuation level. Furthermore, taking into account the time delays in large system, based on a less conservative delay-dependent Lyapunov function approach combining with linear matrix inequalities (LMI) technique, some sufficient conditions for the existence ofH∞robust controller are presented in terms of LMI dependent on the upper bound of time delays. The upper bound of time-delay and minimizedH∞performance index can be obtained by using convex optimization such that the system can be stabilized and for all time delays whose sizes are not larger than the bound. Finally, the effectiveness of the proposed controller is demonstrated through simulation example.

Download Full-text

Spectral Gap of the Largest Eigenvalue of the Normalized Graph Laplacian

Communications in Mathematics and Statistics ◽

10.1007/s40304-020-00222-7 ◽

2021 ◽

Author(s):

Jürgen Jost ◽

Raffaella Mulas ◽

Florentin Münch

Keyword(s):

Lower Bound ◽

Bipartite Graph ◽

Spectral Gap ◽

Complete Bipartite Graph ◽

Graph Laplacian ◽

New Method ◽

Single Edge ◽

Largest Eigenvalue ◽

Complement Graph ◽

The Largest Eigenvalue

AbstractWe offer a new method for proving that the maxima eigenvalue of the normalized graph Laplacian of a graph with n vertices is at least $$\frac{n+1}{n-1}$$ n + 1 n - 1 provided the graph is not complete and that equality is attained if and only if the complement graph is a single edge or a complete bipartite graph with both parts of size $$\frac{n-1}{2}$$ n - 1 2 . With the same method, we also prove a new lower bound to the largest eigenvalue in terms of the minimum vertex degree, provided this is at most $$\frac{n-1}{2}$$ n - 1 2 .

Download Full-text

Free partition functions and an averaged holographic duality

Journal of High Energy Physics ◽

10.1007/jhep01(2021)130 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Nima Afkhami-Jeddi ◽

Henry Cohn ◽

Thomas Hartman ◽

Amirhossein Tajdini

Keyword(s):

Partition Function ◽

Spectral Gap ◽

Central Charge ◽

Three Dimensional ◽

Two Dimensions ◽

Three Dimensions ◽

Partition Functions ◽

General Constraints ◽

Dimensional Gravity ◽

Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Download Full-text

Persistence of the spectral gap for the Landau–Pekar equations

Letters in Mathematical Physics ◽

10.1007/s11005-020-01350-5 ◽

2021 ◽

Vol 111 (1) ◽

Author(s):

Dario Feliciangeli ◽

Simone Rademacher ◽

Robert Seiringer

Keyword(s):

Initial Data ◽

Spectral Gap ◽

Effective Hamiltonian ◽

Adiabatic Theorem ◽

Strongly Coupled

AbstractThe Landau–Pekar equations describe the dynamics of a strongly coupled polaron. Here, we provide a class of initial data for which the associated effective Hamiltonian has a uniform spectral gap for all times. For such initial data, this allows us to extend the results on the adiabatic theorem for the Landau–Pekar equations and their derivation from the Fröhlich model obtained in previous works to larger times.

Download Full-text