The exact convergence rate in the ergodic theorem of Lubotzky–Phillips–Sarnak and a universal lower bound on discrepancies

2021 ◽  
Vol 67 (1) ◽  
pp. 63-94
Author(s):  
Antoine Pinochet Lobos ◽  
Christophe Pittet
Keyword(s):  
Lower Bound ◽  
Convergence Rate ◽  
Ergodic Theorem

Lower bound for the oracle projection posterior convergence rate

2011 ◽  
Vol 81 (2) ◽  
pp. 175-180
Author(s):  
Alexandra Babenko ◽  
Eduard Belitser
Keyword(s):  
Lower Bound ◽  
Convergence Rate

On Exponential Flocking to the Virtual Leader in Network of Agents With Double-Integrator Dynamics

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Hamidreza Tavafoghi Jahromi ◽  
Mohammad Haeri
Keyword(s):  
Lower Bound ◽  
Convergence Rate ◽  
Initial Conditions ◽  
Linear Algorithm ◽  
Calculated Rate ◽  
Virtual Leader ◽  
Double Integrator ◽  
Locally Linear

This paper considers flocking to the virtual leader in network of agents with double-integrator. A locally linear algorithm is employed which guarantees exponential flocking to the virtual leader. A lower bound for flocking rate is calculated which is independent of the initial conditions. Simulations are provided to validate the result and it is shown that the calculated rate is not over bound the actual convergence rate. The effect of coefficients of algorithm is investigated and it is shown that the similar results can be inferred from the calculated formula for the convergence rate.

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