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Commit c7f26305 authored by Florent Chatelain's avatar Florent Chatelain
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"source": [
"## Simulations\n",
"\n",
"$$\\left[\\begin{matrix} 10 & 5.5 \\\\ 5.5 & 15\\end{matrix}\\right]$$\n",
"\n",
"#### Figure 1.\n",
"Eigenvalue distribution $\\nu_n$ of $K$ versus limit measure $\\nu$, for $p=200$, $n=4\\,000$, $x_i\\sim .4 \\mathcal N(\\mu_1,I_p)+.6\\mathcal N(\\mu_2,I_p)$ for \n",
"$[\\mu_1^T,\\mu_2^T]^T \\sim\\mathcal{N}(0, \\frac1p {\\tiny \\left[\\begin{matrix} 10 & 5.5 \\\\ 5.5 & 15\\end{matrix}\\right] } x I_p)$; \n",
"$[\\mu_1^T,\\mu_2^T]^T \\sim\\mathcal{N}(0, \\frac1p {\\tiny \\left[\\begin{matrix} 10 & 5.5 \\\\ 5.5 & 15\\end{matrix}\\right] }\\otimes I_p)$; \n",
"$\\varepsilon_S=.2$, $\\varepsilon_B=.4$. Sample vs theoretical spikes in blue vs red circles. <b>The two \"humps\" remind the semi-circular and Marcenko-Pastur laws.</b>"
]
},
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