(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 151666, 4538]*) (*NotebookOutlinePosition[ 152314, 4560]*) (* CellTagsIndexPosition[ 152270, 4556]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Gessel-Viennot Long Term #9\ \>", "Subsection"], Cell["\<\ \"Actual value\" code\ \>", "Text"], Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(\(GetStartPoint[index_, \ coord_, \ d_]\ := \ If[coord\ \[Equal] \ 1, \ d\ \((index\ - \ 1)\), \ \(-\ d\)\ \((index\ - \ 1)\)];\)\[IndentingNewLine] \(GetEndPoint[index_, \ coord_, length_, \ d_, \ slope_]\ := \ GetStartPoint[index, \ coord, \ d]\ + \ If[coord \[Equal] 1, \ length\ slope, \ length\ \((1\ - \ slope)\)];\)\[IndentingNewLine] \(PathCount[i_, \ j_, \ length_, \ d_, \ slope_]\ := Binomial[ GetEndPoint[j, \ 1, length, \ d, \ slope] - GetStartPoint[i, \ 1, d] + GetEndPoint[j, 2, length, d, slope] - GetStartPoint[i, \ 2, d]\ , GetEndPoint[j, \ 1, length, d, slope] - GetStartPoint[i, \ 1, d]\ ];\)\[IndentingNewLine] \(AllConfigs[count_, length_, \ d_, \ slope_]\ := \ Table[\ PathCount[i, \ j, \ length, \ d, \ slope], \ {i, \ 1, \ count}, \ {j, \ 1, \ count}];\)\[IndentingNewLine] \(Actual[alpha_, \ N_, \ d_, \ paths_] := \(1\/N\) Log[\ Det[\ \((AllConfigs[paths, \ N, d, \ alpha\ ]\ )\)]];\)\)\)\)], "Input"], Cell["\<\ Let me examine large N, 0.5 alpha, fixed paths, large d. 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