Optimal bounds in normal approximation for many interacting worlds
نویسندگان
چکیده
In this paper, we use Stein’s method to obtain optimal bounds, both in Kolmogorov and Wasserstein distance, the normal approximation for empirical distribution of ground state a many-interacting-worlds harmonic oscillator proposed by Hall, Deckert Wiseman (Phys. Rev. X 4 (2014) 041013). Our bounds on distance solve conjecture McKeague Levin (Ann. Appl. Probab. 26 (2016) 2540–2555).
منابع مشابه
L Bounds in Normal Approximation
The zero bias distribution W ∗ of W , defined though the characterizing equation EWf(W ) = σ2Ef ′(W ∗) for all smooth functions f , exists for all W with mean zero and finite variance σ2. For W and W ∗ defined on the same probability space, the L1 distance between F , the distribution function of W with EW = 0 and Var(W ) = 1, and the cumulative standard normal Φ has the simple upper bound ||F ...
متن کاملL1 bounds in normal approximation
The zero bias distribution W * of W , defined though the characterizing equation EW f (W) = σ 2 Ef ′ (W *) for all smooth functions f , exists for all W with mean zero and finite variance σ 2. For W and W * defined on the same probability space, the L 1 distance between F , the distribution function of W with EW = 0 and Var(W) = 1, and the cumulative standard normal Φ has the simple upper bound...
متن کاملStein’s Method, Many Interacting Worlds and Quantum Mechanics
Hall, Deckert and Wiseman (2014) recently proposed that quantum theory can be understood as the continuum limit of a deterministic theory in which there is a large, but finite, number of classical “worlds.” A resulting Gaussian limit theorem for particle positions in the ground state, agreeing with quantum theory, was conjectured in Hall, Deckert and Wiseman (2014) and proven by McKeague and Le...
متن کاملMany-Events Theory for Many-Worlds Interpretation
The probabilistic prediction of quantum theory is mystery. In this paper I solved the mystery by Many-Events Theory. In this theory an absolute value of a wave function is a radius of a new space. This suggests the unification between quantum theory and the theory of relativity.
متن کاملOn the bounds in Poisson approximation for independent geometric distributed random variables
The main purpose of this note is to establish some bounds in Poisson approximation for row-wise arrays of independent geometric distributed random variables using the operator method. Some results related to random sums of independent geometric distributed random variables are also investigated.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Applied Probability
سال: 2023
ISSN: ['1050-5164', '2168-8737']
DOI: https://doi.org/10.1214/21-aap1747