we analyze some properties of the distribution $q_{g,k}$ of the first component in a $k$-tuple chosen uniformly‎ ‎in the set of all the $k$-tuples generating a finite group $g$ (the limiting distribution of the product replacement algorithm)‎. ‎in particular‎, ‎we concentrate our attention on‎ ‎the study of the variation distance $beta_k(g)$ between $q_{g,k}$ and the uniform distribution‎. ‎we ...

today power consumption is considered to be one of the important issues. therefore, its reduction plays a considerable role in developing systems. previous studies have shown that approximately 50% of total power consumption is used in cache memories. there is a direct relationship between power consumption and replacement quantity made in cache. the less the number of replacements is, the less...

The product replacement algorithm is a heuristic designed to generate random group elements. The idea is to run a random walk on generating k-tuples of the group, and then output a random component. The algorithm was designed by Leedham-Green and Soicher ([31]), and further investigated in [12]. It was found to have an outstanding performance, much better than the the previously known algorithm...

‎we investigate two constructions‎ - ‎the replacement and the zig-zag‎ ‎product of graphs‎ - ‎describing several fascinating connections‎ ‎with combinatorics‎, ‎via the notion of expander graph‎, ‎group‎ ‎theory‎, ‎via the notion of semidirect product and cayley graph‎, ‎and‎ ‎with markov chains‎, ‎via the lamplighter random walk‎. ‎many examples‎ ‎are provided‎.

Today power consumption is considered to be one of the important issues. Therefore, its reduction plays a considerable role in developing systems. Previous studies have shown that approximately 50% of total power consumption is used in cache memories. There is a direct relationship between power consumption and replacement quantity made in cache. The less the number of replacements is, the less...

Today power consumption is considered to be one of the important issues. Therefore, its reduction plays a considerable role in developing systems. Previous studies have shown that approximately 50% of total power consumption is used in cache memories. There is a direct relationship between power consumption and replacement quantity made in cache. The less the number of replacements is, the less...

We prove that the product replacement graph on generating k-tuples of a simple group contains a large connected component if k ≥ 3. This is related to the recent conjecture of Diaconis and Graham. As an application, we also prove that the output of the product replacement algorithm (see [CLMNO]) in this case does not have a strong bias.