Manuscript Oai227-A@1 · Oai227-A.tex · section · 7f45f607

Initialization, observables, and convergence

Stage 4: change one hypothesis at a time › Initialization, observables, and convergence · lines 1049–1096

Proposed change	Mathematical effect	Disposition
Proposed change	Mathematical effect	Disposition
Replace $U_{n}$ by $π$	The entrance density becomes one from the start.	This removes the quench-selection problem.
Keep only stationary convergence	One loses the waiting-time variable and uniform-start selection.	Closer to the stationary companion, not all of 227-01.
Drop either named disorder	One no longer compares the two coupling laws.	The universality clause has been weakened.
Replace the mean of spin autocorrelations by magnetization autocorrelation	Cross-spin terms are introduced.	A different observable requires its own argument.
Average disorder before taking the process law	Random conditional means are replaced by annealed averages.	The claimed non-point limiting law is no longer the same object.
Use a mixing-time exponent	Only a distance-to-equilibrium timescale is controlled.	No entrance law or random autocorrelation limit follows.
Use a finite time grid only	Between-grid oscillation is uncontrolled without a modulus.	Finite-dimensional information is not automatically functional.
Use the finite modulus in Lemma lem:modulus at growing $n$	Its constants grow polynomially with $n$ .	It supplies no uniform asymptotic tightness by itself.