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M_real = np.random.randn(Nmatr, N, N) M_imag = np.random.randn(Nmatr, N, N) M = (M_real + 1j * M_imag + M_real.transpose((0, 2, 1)) - 1j * M_imag.transpose((0, 2, 1))) / 2 E = np.linalg.eigvals(M.reshape(Nmatr, N, N)).flatten() elif beta == 4: # Gaussian
Symplectic Ensemble A = np.random.randn(Nmatr, N, N) + 1j * np.random.randn(Nmatr, N, N) B = np.random.randn(Nmatr, N, N) + 1j * np.random.randn(Nmatr, N, N)
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for N in Ns: for beta in betas: if beta == 1: # Gaussian
Orthogonal Ensemble M = np.random.randn(Nmatr, N, N) M = (M + M.transpose((0, 2, 1))) / 2 E = np.linalg.eigvals(M.reshape(Nmatr, N, N)).flatten() elif beta == 2: # Gaussian Unitary Ensemble
332:– You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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M = (M + np.conj(M.transpose((0, 2, 1)))) / 2 E = np.linalg.eigvals(M.reshape(Nmatr, 2 * N, 2 * N)).flatten() if (N, beta) in Es: Es= np.append(Es, E) else: Es = E
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213:# Compute sliding window average window_size = 5 window = np.ones(window_size) / window_size smoothed_heights = np.convolve(bin_heights, window, mode='same')
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bin_heights, bin_borders, _ = ax.hist(xs, bins=500, density=True, color=color, alpha=0.1) bin_centers = bin_borders + np.diff(bin_borders) / 2
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219:# Add plot labels and title ax.set_xlabel('x', fontsize=14) ax.set_ylabel('ρ(x)', fontsize=14) ax.grid(True) ax.legend()
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Please help improve this media file by adding it to one or more categories, so it may be associated with related media files (
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This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
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If the file has been modified from its original state, some details may not fully reflect the modified file.
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The following pages on the
English Knowledge (XXG) use this file (pages on other projects are not listed):
338:– If you remix, transform, or build upon the material, you must distribute your contributions under the
216:# Plot sliding window average ax.plot(bin_centers, smoothed_heights, label=legends, color=color)
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for beta in betas: color = colors E = Es xs = np.real(E) / np.sqrt(2 * beta * N)
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396:{{subst:Please link images|File:Spectral density of gaussian ensembels, N = 1 to 32.png}} ~~~~
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I, the copyright holder of this work, hereby publish it under the following license:
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legends = {1: "GOE", 2: "GUE", 4: "GSE"} colors = {1: "blue", 2: "red", 4: "green"}
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of matrices are diagonalized, and the eigenvalues are collected in the vector E
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226:$ , with N = {} to {}'.format(Ns, Ns), fontsize=18, y=1.04) plt.show()
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Uploaded while editing "Random matrix" on en.wikipedia.org
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The following condition selects the desired ensemble: a number Nmatr
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Click on a date/time to view the file as it appeared at that time.
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Creative
Commons Attribution-ShareAlike 4.0 International
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Add a one-line explanation of what this file represents
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Spectral density of gaussian ensembels, N = 1 to 32.png
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plt.tight_layout() fig.suptitle(r'Eigenvalues $ /\sqrt
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Commons is a freely licensed media file repository.
146:import numpy as np import matplotlib.pyplot as plt
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804:Matplotlib version3.7.1, https://matplotlib.org/
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195:fig, axs = plt.subplots(2, 3, figsize=(18, 9))
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355:Creative Commons Attribution-Share Alike 4.0
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204:row = i // 3 col = i % 3 ax = axs
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186:-np.conj(B), np.conj(A)
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99:. Information from its
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110:You can help
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659:17 May 2023
552:copyrighted
336:share alike
330:attribution
238:17 May 2023
132:Description
769:File usage
726:Dimensions
678:media type
468:some value
144:```python
27:File usage
824:39.37 dpc
816:39.37 dpc
723:Thumbnail
720:Date/Time
693:image/png
644:inception
267:Licensing
141:English:
76:image/png
784:Metadata
752:(258 KB)
412:Captions
319:to remix
313:to share
304:license.
248:Own work
32:Metadata
737:current
732:Comment
453:creator
436:depicts
416:English
124:Summary
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254:Author
244:Source
729:User
387:how?
361:true
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234:Date
182:A, B
17:File
508:URL
228:```
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
