C, 328 585 611 615 623 673 707 bytes

p[256][256]={0};char*X="p[256][256]={0};char*X=%c%s%c,Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;j=*Y;while(c=j)for(putchar(c);;)if(rand()>>16<p[c][++j])break;}",Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;j=*Y;while(c=j)for(putchar(c);;)if(rand()>>16<p[c][++j])break;}

01  p[256][256]={0};
02  char*X="p[256][256]={0};char*X=%c%s%c,Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;j=*Y;while(c=j)for(putchar(c);;)if(rand()>>16<p[c][++j])break;}",
03  Y[999],c,j,*a;
04  main(){
05      sprintf(Y,X,34,X,34);
06      for(a=Y;*a;a++) p[*a][*(a+1)]++;
07      j=*Y;
08      while(c=j)
09          for(putchar(c);;)
10              if(rand()>>16 < p[c][++j])
11                  break;
12  }

The variable p[][] will contain the occurrences of each character following another. X contains the entire source, with %c%s%c instead of the assignment for X. The %c characters will be replaced with 64, the double quotation mark.

Line 06 tallies the occurrences of one character following another and starts the Markov model at the first character of the program ('p').

The while loop from 08 to 11 first outputs the current state of the Markov model, then finds the next state. A state is chosen as the next transition if the next random number is less than the number of occurrences for that state.

I was able to save bytes by using sprintf over my original string-copying.

Increasing the constant 16 on line 10 can decrease the runtime, but it makes the results less random.

p[++);ar()iforile()in(Y;)putfor(aind(c,X,*a+j=j,c][c,*an(arilear(prea+16])putc])>1)>16][c=%c,*X,j=*ak;f(Y;j)fora+j]=j][256<pre(a;a;f(r*ar(Y;fore()>>>16]++j][256<putc][256<putc={sp[256]){0};j],j);}",*X,j],Y[c);a++j,34,X,c%sputf(c)fora],X="p[*ain();c]+1)>>>>1)>1);;arile();f(Y;a;f()>16]={0};){0};wha;j=Y;marilea+1)ind(Y;;);whar(r(a=*ar(r(a+){sputf()>>16][*a]+j,j,X,X,c);j=%chaile(a;;}

C, 306 328 585 611 615 623 673 707 bytes

p[256][256]={0};char*X="p[256][256]={0};char*X=%c%s%c,Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;for(j=*Y;putchar(c=j);)while(p[c][++j]<<16<rand());}",Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;for(j=*Y;putchar(c=j);)while(p[c][++j]<<16<rand());}

01  p[256][256]={0};
02  char*X="p[256][256]={0};char*X=%c%s%c,Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;for(j=*Y;putchar(c=j);)while(p[c][++j]<<16<rand());}",
03  Y[999],c,j,*a;
04  main(){
05      sprintf(Y,X,34,X,34);
06      for(a=Y;*a;a++)p[*a][*(a+1)]++;
07      for(j=*Y;putchar(c=j);)
08          while(p[c][++j]<<16<rand());
09  }

Explanation

Line 01: p[][] holds the counts of one character following another.

Line 02: X contains the program's source, escaped with %c%s%c.

Line 03: Y will contain the program's literal source. c, j, *a are counting variables.

Line 05: Set Y to contain the quine.

Line 06: Count letter occurrences in p[][].

Line 07: Print the current state.

Line 08: Find the next character randomly, proportional to the counts in p[][].

p[++);p[99]=Y;putfor(aind(a++j,*a+j=j,c][c,*an(arile(pr*Y,Y[256]<<1);)][*Y,Y;)wha+++j=*aintfor*Y;prin(a+j]=j][256<1)pr(a;a;f(p[char(Y;for());};a;ma;ma=%s%chain(Y;ar(j][256<<<1)p[256<<raile(cha][9]<rin(j,34,34,Y[256]+j,Y,34,Y,c=Y,*a;*a;for(){0}

C, 328 585 611 615 623 673 707 bytes

Source code:

p[256][256]={0};char*X="p[256][256]={0};char*X=%c%s%c,Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;j=*Y;while(c=j)for(putchar(c);;)if(rand()>>16<p[c][++j])break;}",Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;j=*Y;while(c=j)for(putchar(c);;)if(rand()>>16<p[c][++j])break;}

With newlines and whitespace added for legibility/explanation:

01  p[256][256]={0};
02  char*X="p[256][256]={0};char*X=%c%s%c,Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;j=*Y;while(c=j)for(putchar(c);;)if(rand()>>16<p[c][++j])break;}",
03  Y[999],c,j,*a;
04  main(){
05      sprintf(Y,X,34,X,34);
06      for(a=Y;*a;a++) p[*a][*(a+1)]++;
07      j=*Y;
08      while(c=j)
09          for(putchar(c);;)
10              if(rand()>>16 < p[c][++j])
11                  break;
12  }

The variable p[][] will contain the occurrences of each character following another. X contains the entire source, with %c%s%c instead of the assignment for X. The %c characters will be replaced with 64, the double quotation mark.

Line 06 tallies the occurrences of one character following another and starts the Markov model at the first character of the program ('p').

The while loop from 08 to 11 first outputs the current state of the Markov model, then finds the next state. A state is chosen as the next transition if the next random number is less than the number of occurrences for that state.

I was able to save bytes by using sprintf over my original string-copying.

Increasing the constant 16 in line 10 can decrease the runtime, but it makes the results less random.

Sample output:

p[++);ar()iforile()in(Y;)putfor(aind(c,X,*a+j=j,c][c,*an(arilear(prea+16])putc])>1)>16][c=%c,*X,j=*ak;f(Y;j)fora+j]=j][256<pre(a;a;f(r*ar(Y;fore()>>>16]++j][256<putc][256<putc={sp[256]){0};j],j);}",*X,j],Y[c);a++j,34,X,c%sputf(c)fora],X="p[*ain();c]+1)>>>>1)>1);;arile();f(Y;a;f()>16]={0};){0};wha;j=Y;marilea+1)ind(Y;;);whar(r(a=*ar(r(a+){sputf()>>16][*a]+j,j,X,X,c);j=%chaile(a;;}

C, 328 585 611 615 623 673 707 bytes

Source code:

p[256][256]={0};char*X="p[256][256]={0};char*X=%c%s%c,Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;j=*Y;while(c=j)for(putchar(c);;)if(rand()>>16<p[c][++j])break;}",Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;j=*Y;while(c=j)for(putchar(c);;)if(rand()>>16<p[c][++j])break;}

With newlines and whitespace added for legibility/explanation:

01  p[256][256]={0};
02  char*X="p[256][256]={0};char*X=%c%s%c,Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;j=*Y;while(c=j)for(putchar(c);;)if(rand()>>16<p[c][++j])break;}",
03  Y[999],c,j,*a;
04  main(){
05      sprintf(Y,X,34,X,34);
06      for(a=Y;*a;a++) p[*a][*(a+1)]++;
07      j=*Y;
08      while(c=j)
09          for(putchar(c);;)
10              if(rand()>>16 < p[c][++j])
11                  break;
12  }

The variable p[][] will contain the occurrences of each character following another. X contains the entire source, with %c%s%c instead of the assignment for X. The %c characters will be replaced with 64, the double quotation mark.

Line 06 tallies the occurrences of one character following another and starts the Markov model at the first character of the program ('p').

The while loop from 08 to 11 first outputs the current state of the Markov model, then finds the next state. A state is chosen as the next transition if the next random number is less than the number of occurrences for that state.

I was able to save bytes by using sprintf over my original string-copying.

Increasing the constant 16 on line 10 can decrease the runtime, but it makes the results less random.

Sample output:

p[++);ar()iforile()in(Y;)putfor(aind(c,X,*a+j=j,c][c,*an(arilear(prea+16])putc])>1)>16][c=%c,*X,j=*ak;f(Y;j)fora+j]=j][256<pre(a;a;f(r*ar(Y;fore()>>>16]++j][256<putc][256<putc={sp[256]){0};j],j);}",*X,j],Y[c);a++j,34,X,c%sputf(c)fora],X="p[*ain();c]+1)>>>>1)>1);;arile();f(Y;a;f()>16]={0};){0};wha;j=Y;marilea+1)ind(Y;;);whar(r(a=*ar(r(a+){sputf()>>16][*a]+j,j,X,X,c);j=%chaile(a;;}

C, 336 585 611 615 623 673 707 bytes

p[256][256]={0};char*X="p[256][256]={0};char*X=%c%s%c,Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;j=*Y;while(c=j){putchar(c);for(;;j++)if(rand()>>16<p[c][j])break;}}",Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;j=*Y;while(c=j){putchar(c);for(;;j++)if(rand()>>16<p[c][j])break;}}

01  p[256][256]={0};
02  char*X="p[256][256]={0};char*X=%c%s%c,Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;j=*Y;while(c=j){putchar(c);for(;;j++)if(rand()>>16<p[c][j])break;}}",
03  Y[999],c,j,*a;
04  main(){
05      sprintf(Y,X,34,X,34);
06      for(a=Y;*a;a++) p[*a][*(a+1)]++;
07      j=*Y;
08      while(c=j){
09          putchar(c);
10          for(;;j++)
11              if(rand()>>16 < p[c][j])
12                  break;
13      }
14  }

The while loop from 08 to 13 first outputs the current state of the Markov model, then finds the next state. A state is chosen as the next transition if the next random number is less than the number of occurrences for that state.

I was able to save a bunch of bytes by using sprintf.

p[j]+;;*a;forintforear(c=Y;;whif(;;j,j+;j][256<pr(Y;j,X,X,cha][j+)in(cha;fora+++;cha=j=j]=*X={0}}}}"p[*ain()p[9]={s%c)p[*antc,chin(c][c%c%sp[*ar*X=Y[*a;j,34,Y;f();j+){0}

C, 328 585 611 615 623 673 707 bytes

p[256][256]={0};char*X="p[256][256]={0};char*X=%c%s%c,Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;j=*Y;while(c=j)for(putchar(c);;)if(rand()>>16<p[c][++j])break;}",Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;j=*Y;while(c=j)for(putchar(c);;)if(rand()>>16<p[c][++j])break;}

01  p[256][256]={0};
02  char*X="p[256][256]={0};char*X=%c%s%c,Y[999],c,j,*a;main(){sprintf(Y,X,34,X,34);for(a=Y;*a;a++)p[*a][*(a+1)]++;j=*Y;while(c=j)for(putchar(c);;)if(rand()>>16<p[c][++j])break;}",
03  Y[999],c,j,*a;
04  main(){
05      sprintf(Y,X,34,X,34);
06      for(a=Y;*a;a++) p[*a][*(a+1)]++;
07      j=*Y;
08      while(c=j)
09          for(putchar(c);;)
10              if(rand()>>16 < p[c][++j])
11                  break;
12  }

The while loop from 08 to 11 first outputs the current state of the Markov model, then finds the next state. A state is chosen as the next transition if the next random number is less than the number of occurrences for that state.

I was able to save bytes by using sprintf over my original string-copying.

Increasing the constant 16 in line 10 can decrease the runtime, but it makes the results less random.

p[++);ar()iforile()in(Y;)putfor(aind(c,X,*a+j=j,c][c,*an(arilear(prea+16])putc])>1)>16][c=%c,*X,j=*ak;f(Y;j)fora+j]=j][256<pre(a;a;f(r*ar(Y;fore()>>>16]++j][256<putc][256<putc={sp[256]){0};j],j);}",*X,j],Y[c);a++j,34,X,c%sputf(c)fora],X="p[*ain();c]+1)>>>>1)>1);;arile();f(Y;a;f()>16]={0};){0};wha;j=Y;marilea+1)ind(Y;;);whar(r(a=*ar(r(a+){sputf()>>16][*a]+j,j,X,X,c);j=%chaile(a;;}