File:Rate function of Tracy–Widom large deviation.svg
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Summary
| Description |
English: Rate function of Tracy–Widom large deviation
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plt.plot(w_minus, phi_minus_approx_values, 'r--', label=r'$\Phi_-(w) \sim �rac{1}{6\sqrt{2}} (\sqrt{2} - w)^3matplotlib codeimport matplotlib.pyplot as plt
import numpy as np
def phi_minus(w):
return (1/108) * (36*w**2 - w**4 - (15*w + w**3)*np.sqrt(w**2 + 6) + 27*(np.log(18) - 2*np.log(w + np.sqrt(w**2 + 6))))
def phi_plus(w):
return 0.5*w*np.sqrt(w**2 - 2) + np.log((w - np.sqrt(w**2 - 2))/np.sqrt(2))
def phi_minus_approx(w):
return (1/(6*np.sqrt(2))) * (np.sqrt(2) - w)**3
def phi_plus_approx(w):
return (2**(7/4)/3) * (w - np.sqrt(2))**(3/2)
w_minus = np.linspace(-1, np.sqrt(2), 500)
w_plus = np.linspace(np.sqrt(2), 3, 500)
phi_minus_values = phi_minus(w_minus)
phi_plus_values = phi_plus(w_plus)
phi_minus_approx_values = phi_minus_approx(w_minus)
phi_plus_approx_values = phi_plus_approx(w_plus)
plt.figure(figsize=(8, 6))
plt.plot(w_minus, phi_minus_values, label=r'$\Phi_-(w)
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| Source | Own work |
| Author |
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plt.plot(w_plus, phi_plus_approx_values, 'g--', label=r'$\Phi_+(w) \sim �rac{2^{7/4}}{3} (w - \sqrt{2})^{3/2}}}) plt.xlabel('w') plt.ylabel(r'$\Phi(w)}}) plt.title(r'Rate function of Tracy–Widom large deviation') plt.axvline(x=np.sqrt(2), color='k', linestyle='--') plt.legend() plt.grid(True) plt.savefig('Rate function of Tracy–Widom large deviation.svg') plt.show() }} }} |date=2025-02-03 |source=Own work |author=Cosmia Nebula }}
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 05:22, 4 February 2025 | | 768 × 576 (42 KB) | Cosmia Nebula | Uploaded while editing "Tracy–Widom distribution" on en.wikipedia.org |
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