with(LinearAlgebra):

P:= Matrix([ [ 0 , p , 0 , 1 - p ], [ 1 - p , 0 , p , 0 ], [ 0 , 1 - p , 0 , p ], [ p , 0 , 1 - p , 0 ] ]);

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factor(Determinant(P));

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

subs(p=1/2,MatrixPower(P,3));

Assume (p < 1/2); Assume (p >0);

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

(v,B) :=Eigenvectors(P);

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

B := simplify(B);

NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USJCRigvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GKC8lJXNpemVHUSMxMkYoLyUlYm9sZEdRJmZhbHNlRigvJSdpdGFsaWNHUSV0cnVlRigvJSp1bmRlcmxpbmVHRjgvJSpzdWJzY3JpcHRHRjgvJSxzdXBlcnNjcmlwdEdGOC8lK2ZvcmVncm91bmRHUSpbMCwwLDI1NV1GKC8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRigvJSdvcGFxdWVHRjgvJStleGVjdXRhYmxlR0Y4LyUpcmVhZG9ubHlHRjsvJSljb21wb3NlZEdGOC8lKmNvbnZlcnRlZEdGOC8lK2ltc2VsZWN0ZWRHRjgvJSxwbGFjZWhvbGRlckdGOC8lMGZvbnRfc3R5bGVfbmFtZUdRKjJEfk91dHB1dEYoLyUqbWF0aGNvbG9yR0ZELyUvbWF0aGJhY2tncm91bmRHRkcvJStmb250ZmFtaWx5R0YyLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGKC8lKW1hdGhzaXplR0Y1LUkjbW9HRiU2M1EjOj1GKC8lJWZvcm1HUSZpbmZpeEYoLyUmZmVuY2VHRjgvJSpzZXBhcmF0b3JHRjgvJSdsc3BhY2VHUS90aGlja21hdGhzcGFjZUYoLyUncnNwYWNlR0ZbcC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobWF4c2l6ZUdRKWluZmluaXR5RigvJShtaW5zaXplR1EiMUYoLyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJTBmb250X3N0eWxlX25hbWVHRlgvJSVzaXplR0Y1LyUrZm9yZWdyb3VuZEdGRC8lK2JhY2tncm91bmRHRkctRiQ2JS1GX282M1EiW0YoL0Zjb1EncHJlZml4RigvRmZvRjtGZ28vRmpvUS50aGlubWF0aHNwYWNlRigvRl1wRl9yL0ZfcEY7RmBwRmJwRmVwRmhwRmpwRlxxRl5xRmBxRmJxRmRxLUYkNiMtSSdtdGFibGVHRiU2Ji1JJG10ckdGJTYmLUkkbXRkR0YlNiMtSSNtbkdGJTY5RmdwRjBGM0Y2L0Y6RjhGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduL0ZqblEnbm9ybWFsRihGXG8tRltzNiMtRl5zNjlRKSZtaW51czsxRihGMEYzRjZGYHNGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmFzRlxvLUZbczYjLUZeczY5USJJRihGMEYzRjZGYHNGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmFzRlxvLUZbczYjLUYkNiQtRl9vNjNRKiZ1bWludXMwO0YoRltyRmVvRmdvL0Zqb1EkMGVtRigvRl1wRmV0Rl5wRmBwRmJwRmVwRmhwRmpwRlxxRl5xRmBxRmJxRmRxRmpzLUZocjYmRmpyRmpyRmNzRmNzLUZocjYmRmpyRmNzRl10RmhzLUZocjYmRmpyRmpyRmpyRmpyLUZfbzYzUSJdRigvRmNvUShwb3N0Zml4RihGXXJGZ29GXnIvRl1wUTJ2ZXJ5dGhpbm1hdGhzcGFjZUYoRmFyRmBwRmJwRmVwRmhwRmpwRlxxRl5xRmBxRmJxRmRxNyMtX0YpSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJCR0YoLUknUlRBQkxFR0YoNiUiKTcyajstSSdNQVRSSVhHRig2IzcmNyYiIiIhIiJeI0ZldiwkRmd2RmZ2NyZGZXZGZXZGZnZGZnY3JkZldkZmdkZodkZndjcmRmV2RmV2RmV2RmV2SSdNYXRyaXhHNiQlKnByb3RlY3RlZEdGKjcjLUZcdzYjL0kkJWlkR0YoRl92

MatrixMatrixMultiply(P,B);

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

Lambda:=DiagonalMatrix(v);

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

MatrixAdd(MatrixMatrixMultiply(P,B),-MatrixMatrixMultiply(B,Lambda));

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

simplify(%);

invB:=MatrixInverse(B);

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sP:=MatrixMatrixMultiply(MatrixMatrixMultiply(invB,P),B);

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

sP := simplify(sP);simplify(Determinant(sP));

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

sPN:=MatrixPower(sP,N);

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

P_N := simplify(MatrixMatrixMultiply(MatrixMatrixMultiply(B,sPN),invB)):

Let's check fro periodicity.

for k from 1 to 4 do sPk :=MatrixPower(sP,k): print(simplify(MatrixMatrixMultiply(MatrixMatrixMultiply(B,sPk),invB))); od:

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

Period 2!

Z:= IdentityMatrix(4)-s*P; factor(Determinant(Z));

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We compute p_{i,i}(s) and using the renewal equation compute the derivative of f_{i,i}. This gives the mean recurrence times.

for m from 1 to 4 do pii[m] := unapply(simplify(expand(MatrixInverse(Z)[m,m])),s); limit(pii[m](s),s=1,left); simplify(expand(-diff(1/pii[m](s),s))); limit(%,s=1,left); od;

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

The renewal theorem tells us that the limit of of the coefficient of p_{i,i)(s) approaches

1/(mean recurrence time) if our Markov chain is aperiodic. As we saw above, it has period 2.

Thus odd coeffs are zero!, but even coeffs over 2 (i.e., (nth coeff+(n+1)st coeff)/2 -> 1/(mean recurrence time) .

for j from 1 to 9 do evalf(subs(p=1/3,coeff(taylor(pii[2](s),s=0,30),s^(2*j))/2)); od;

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