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| __TOC__
| | [[File:SpanishFlag.png|24px|right|link=Bienvenido]] |
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| <strong>MediaWiki has been installed.</strong>
| | =Welcome!= |
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| Consult the [//meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.
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| Let's add a link to my [[Blog|blog]]
| | Welcome to my personal website. |
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| | I set up this website in October 2016, mainly as the answer to an |
| | everlasting craving to express my thoughts in a written form. Over the years, however, this page turned into a reservoir where all the information regarding my academic life were collected. Thus, here you will find sections for my [[Publications|publications]], my [[Activities |research interests]], the [[Funding|funding]] that I've received to carry on researching, the popular science [https://pop-science.camilopez.org blogs], and last but not least, about the [[Teaching | teaching]] that I've done. |
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| $\newcommand{\Re}{\mathrm{Re}\,}
| | This site also contains pages about the technical details of the |
| \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)}
| | tools I use on a daily basis, such as [[Emacs|emacs]], |
| \newcommand{\ket}[1]{\vert #1\range}$
| | [[Latex|$\LaTeX$]] and [[Mathematica|Mathematica]]. Please, feel |
| | free to visit them. |
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|
| Take a look at this beautifully typesetted equation:
| | The language of this website is the universal language of science |
| \begin{equation}
| | and technology: English. However, as my native language is |
| p(n) = \mathcal{C}_n\times
| | Spanish, some pages are going to be written Spanish (too). |
| {}_1\!F_2\left(n+1;\frac{2n+1}{2}+\frac{\Gamma_\sigma}{\Gamma},
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| n+\frac{\Gamma_\sigma}{\Gamma};
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| -\frac{P_\sigma} {2\Gamma}
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| \right)\times \ket{\alpha}
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| \end{equation}
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| | | You may want to go directly to the [[Curriculum_Vitae|science]] |
| | | section. Perhaps the [[Contact|contact]] page? Or maybe you |
| We consider, for various values of $s$, the $n$-dimensional integral
| | want to try a [http://camilopez.org/wiki/Special:Random random page]. |
| \begin{align}
| |
| \label{def:Wns}
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| W_n (s)
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| &:=
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| \int_{[0, 1]^n}
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| \left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x}
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| \end{align}
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| which occurs in the theory of uniform random walk integrals in the plane,
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| where at each step a unit-step is taken in a random direction. As such,
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| the integral \eqref{def:Wns} expresses the $s$-th moment of the distance | |
| to the origin after $n$ steps.
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| | |
| By experimentation and some sketchy arguments we quickly conjectured and
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| strongly believed that, for $k$ a nonnegative integer
| |
| \begin{align}
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| \label{eq:W3k}
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| W_3(k) &= \Re \, \pFq 32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}.
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| \end{align}
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| Appropriately defined, \eqref{eq:W3k} also holds for negative odd integers.
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| The reason for \eqref{eq:W3k} was long a mystery, but it will be explained
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| at the end of the paper.
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| | |
| == First Section ==
| |
| | |
| === First Subsection ===
| |
| | |
| ==== First subsubsection ====
| |
| | |
| <m>x^2</m>
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| <i class="fa fa-file-pdf-o fa-2x" aria-hidden="true"></i> CV file
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| <i class="fa fa-camera-retro"></i> fa-camera-retro
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| <a class="list-group-item" href="#"><i class="fa fa-home fa-fw" aria-hidden="true"></i> Home</a>
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| <a class="list-group-item" href="#"><i class="fa fa-book fa-fw" aria-hidden="true"></i> Library</a>
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| <a class="list-group-item" href="#"><i class="fa fa-pencil fa-fw" aria-hidden="true"></i> Applications</a>
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| <a class="list-group-item" href="#"><i class="fa fa-cog fa-fw" aria-hidden="true"></i> Settings</a>
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| <div class="list-group">
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| <a class="list-group-item" href="#"><i class="fa fa-home fa-fw" aria-hidden="true"></i> Home</a>
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| <a class="list-group-item" href="#"><i class="fa fa-book fa-fw" aria-hidden="true"></i> Library</a>
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| <a class="list-group-item" href="#"><i class="fa fa-pencil fa-fw" aria-hidden="true"></i> Applications</a>
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| <a class="list-group-item" href="#"><i class="fa fa-cog fa-fw" aria-hidden="true"></i> Settings</a>
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| <ul class="fa-ul">
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| <li><i class="fa-li fa fa-check-square"></i>List icons</li>
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| <li><i class="fa-li fa fa-check-square"></i>can be used</li>
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| <li><i class="fa-li fa fa-spinner fa-spin"></i>as bullets</li>
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| <li><i class="fa-li fa fa-square"></i>in lists</li>
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| </ul>
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| | |
| <i class="fa fa-quote-left fa-3x fa-pull-left fa-border" aria-hidden="true"></i>
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| ...tomorrow we will run faster, stretch out our arms farther...
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| And then one fine morning— So we beat on, boats against the
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| current, borne back ceaselessly into the past.
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| | |
| == Getting started ==
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Welcome!
Welcome to my personal website.
I set up this website in October 2016, mainly as the answer to an
everlasting craving to express my thoughts in a written form. Over the years, however, this page turned into a reservoir where all the information regarding my academic life were collected. Thus, here you will find sections for my publications, my research interests, the funding that I've received to carry on researching, the popular science blogs, and last but not least, about the teaching that I've done.
This site also contains pages about the technical details of the
tools I use on a daily basis, such as emacs,
$\LaTeX$ and Mathematica. Please, feel
free to visit them.
The language of this website is the universal language of science
and technology: English. However, as my native language is
Spanish, some pages are going to be written Spanish (too).
You may want to go directly to the science
section. Perhaps the contact page? Or maybe you
want to try a random page.
