.. _sphx_glr_api_gallery_rmt_edge_statistics:

Edge statistics
---------------

Fluctuations of the extreme eigenvalues: the Tracy-Widom soft-edge laws
for the largest eigenvalue of the GOE, GUE, and GSE.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="For the Gaussian beta-ensembles GOE (\beta=1), GUE (\beta=2), and GSE (\beta=4), the bulk of the n-eigenvalue spectrum fills the semicircle [-2, 2], but the largest eigenvalue \lambda_{\max} fluctuates above the edge 2 on a much finer scale than the bulk spacing: rescaling">

.. only:: html

  .. image:: /api/gallery/rmt/edge_statistics/images/thumb/sphx_glr_plot_tracy_widom_soft_edge_thumb.png
    :alt:

  :doc:`/api/gallery/rmt/edge_statistics/plot_tracy_widom_soft_edge`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Tracy-Widom Soft-Edge Laws</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/rmt/edge_statistics/plot_tracy_widom_soft_edge