Mrthfx

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1

I have the following:

documentclass[11pt, a4paper]{report}

usepackage{bm}

usepackage{amsfonts, graphicx, verbatim, amsmath,amssymb, amsthm}

usepackage{color}

usepackage{array}

usepackage{setspace}% if you must (for double spacing thesis)

usepackage{fancyhdr}

usepackage{enumitem}

usepackage{tikz}

usepackage{parskip}

usepackage{lipsum}

begin{document}

begin{example} 

Consider a random walk on the $n$-cycle. Let $Omega = mathbb{Z}_n = lbrace 0, 1, 2, cdots, n-1 rbrace$ be the set of remainders modulo $n$. Also consider the transition matrix:

[

P(x,y) = 

begin{cases} 

frac{1}{2} & text{if } y=x+1;; (mod;n)\

frac{1}{2} & text{if } y=x-1;; (mod;n)\

0 & text{otherwise}

end{cases}

]



The associated Markov chain $X_t$ is called a random walk on the $n$-cycle. The sates can be visualised as equally spaced nodes arranged in a circle(see figure 1.1)

end{example}



begin{figure}[htbp]

    centering

    begin{tikzpicture}

    foreach i in {90,54,...,-234} {

        draw[ultra thick] (i:2)--({i-36}:2);

    }

    foreach i in {90,18,...,-198} {

        draw[fill=black] (i:2) circle (1.25mm);

    }

    foreach i in {54,-18,...,-234} {

        draw[fill=white] (i:2) circle (1.25mm);

    }

    begin{scope}[xshift=5cm]

    foreach i in {90,50,...,-230} {

        draw[ultra thick] (i:2)--({i-40}:2);

        draw[fill=black] (i:2) circle (1.25mm);

    }

    end{scope}

    end{tikzpicture}

    caption{Random walk on $mathbb{Z}_10$ is periodic, since every step

goes from an even state to an odd state, or vice-versa. Random

walk on $mathbb{Z}_9$ is aperiodic.}

    label{my:figure}

end{figure}

end{document}

now I want to adjust the spacing in the caption in the sense that i want to "push it into the middle", but I don't know how to proceed.

spacing captions

share

asked 3 mins ago

MathMath

114

New contributor

Math is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

add a comment | 

1

I have the following:

documentclass[11pt, a4paper]{report}

usepackage{bm}

usepackage{amsfonts, graphicx, verbatim, amsmath,amssymb, amsthm}

usepackage{color}

usepackage{array}

usepackage{setspace}% if you must (for double spacing thesis)

usepackage{fancyhdr}

usepackage{enumitem}

usepackage{tikz}

usepackage{parskip}

usepackage{lipsum}

begin{document}

begin{example} 

Consider a random walk on the $n$-cycle. Let $Omega = mathbb{Z}_n = lbrace 0, 1, 2, cdots, n-1 rbrace$ be the set of remainders modulo $n$. Also consider the transition matrix:

[

P(x,y) = 

begin{cases} 

frac{1}{2} & text{if } y=x+1;; (mod;n)\

frac{1}{2} & text{if } y=x-1;; (mod;n)\

0 & text{otherwise}

end{cases}

]



The associated Markov chain $X_t$ is called a random walk on the $n$-cycle. The sates can be visualised as equally spaced nodes arranged in a circle(see figure 1.1)

end{example}



begin{figure}[htbp]

    centering

    begin{tikzpicture}

    foreach i in {90,54,...,-234} {

        draw[ultra thick] (i:2)--({i-36}:2);

    }

    foreach i in {90,18,...,-198} {

        draw[fill=black] (i:2) circle (1.25mm);

    }

    foreach i in {54,-18,...,-234} {

        draw[fill=white] (i:2) circle (1.25mm);

    }

    begin{scope}[xshift=5cm]

    foreach i in {90,50,...,-230} {

        draw[ultra thick] (i:2)--({i-40}:2);

        draw[fill=black] (i:2) circle (1.25mm);

    }

    end{scope}

    end{tikzpicture}

    caption{Random walk on $mathbb{Z}_10$ is periodic, since every step

goes from an even state to an odd state, or vice-versa. Random

walk on $mathbb{Z}_9$ is aperiodic.}

    label{my:figure}

end{figure}

end{document}

now I want to adjust the spacing in the caption in the sense that i want to "push it into the middle", but I don't know how to proceed.

spacing captions

share

asked 3 mins ago

MathMath

114

New contributor

Math is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

add a comment | 

I have the following:

documentclass[11pt, a4paper]{report}

usepackage{bm}

usepackage{amsfonts, graphicx, verbatim, amsmath,amssymb, amsthm}

usepackage{color}

usepackage{array}

usepackage{setspace}% if you must (for double spacing thesis)

usepackage{fancyhdr}

usepackage{enumitem}

usepackage{tikz}

usepackage{parskip}

usepackage{lipsum}

begin{document}

begin{example} 

Consider a random walk on the $n$-cycle. Let $Omega = mathbb{Z}_n = lbrace 0, 1, 2, cdots, n-1 rbrace$ be the set of remainders modulo $n$. Also consider the transition matrix:

[

P(x,y) = 

begin{cases} 

frac{1}{2} & text{if } y=x+1;; (mod;n)\

frac{1}{2} & text{if } y=x-1;; (mod;n)\

0 & text{otherwise}

end{cases}

]



The associated Markov chain $X_t$ is called a random walk on the $n$-cycle. The sates can be visualised as equally spaced nodes arranged in a circle(see figure 1.1)

end{example}



begin{figure}[htbp]

    centering

    begin{tikzpicture}

    foreach i in {90,54,...,-234} {

        draw[ultra thick] (i:2)--({i-36}:2);

    }

    foreach i in {90,18,...,-198} {

        draw[fill=black] (i:2) circle (1.25mm);

    }

    foreach i in {54,-18,...,-234} {

        draw[fill=white] (i:2) circle (1.25mm);

    }

    begin{scope}[xshift=5cm]

    foreach i in {90,50,...,-230} {

        draw[ultra thick] (i:2)--({i-40}:2);

        draw[fill=black] (i:2) circle (1.25mm);

    }

    end{scope}

    end{tikzpicture}

    caption{Random walk on $mathbb{Z}_10$ is periodic, since every step

goes from an even state to an odd state, or vice-versa. Random

walk on $mathbb{Z}_9$ is aperiodic.}

    label{my:figure}

end{figure}

end{document}

now I want to adjust the spacing in the caption in the sense that i want to "push it into the middle", but I don't know how to proceed.

spacing captions

share

asked 3 mins ago

MathMath

114

New contributor

Math is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

documentclass[11pt, a4paper]{report}

usepackage{bm}

usepackage{amsfonts, graphicx, verbatim, amsmath,amssymb, amsthm}

usepackage{color}

usepackage{array}

usepackage{setspace}% if you must (for double spacing thesis)

usepackage{fancyhdr}

usepackage{enumitem}

usepackage{tikz}

usepackage{parskip}

usepackage{lipsum}

begin{document}

begin{example} 

Consider a random walk on the $n$-cycle. Let $Omega = mathbb{Z}_n = lbrace 0, 1, 2, cdots, n-1 rbrace$ be the set of remainders modulo $n$. Also consider the transition matrix:

[

P(x,y) = 

begin{cases} 

frac{1}{2} & text{if } y=x+1;; (mod;n)\

frac{1}{2} & text{if } y=x-1;; (mod;n)\

0 & text{otherwise}

end{cases}

]



The associated Markov chain $X_t$ is called a random walk on the $n$-cycle. The sates can be visualised as equally spaced nodes arranged in a circle(see figure 1.1)

end{example}



begin{figure}[htbp]

    centering

    begin{tikzpicture}

    foreach i in {90,54,...,-234} {

        draw[ultra thick] (i:2)--({i-36}:2);

    }

    foreach i in {90,18,...,-198} {

        draw[fill=black] (i:2) circle (1.25mm);

    }

    foreach i in {54,-18,...,-234} {

        draw[fill=white] (i:2) circle (1.25mm);

    }

    begin{scope}[xshift=5cm]

    foreach i in {90,50,...,-230} {

        draw[ultra thick] (i:2)--({i-40}:2);

        draw[fill=black] (i:2) circle (1.25mm);

    }

    end{scope}

    end{tikzpicture}

    caption{Random walk on $mathbb{Z}_10$ is periodic, since every step

goes from an even state to an odd state, or vice-versa. Random

walk on $mathbb{Z}_9$ is aperiodic.}

    label{my:figure}

end{figure}

end{document}

share

asked 3 mins ago

MathMath

114

New contributor

Math is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share

asked 3 mins ago

MathMath

114

New contributor

Math is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 3 mins ago

MathMath

114

New contributor

Math is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 3 mins ago

MathMath

114