<i>SU</i>(<i>d</i>)-Biinvariant Random Walks on <img src="/fulltext-image.asp?format=htmlnonpaginated&src=28213723648W06Q8_html\10440_2006_9035_Article_IEq2.gif" border="0" alt="$$SL\,{\left( {d,\,\mathbb{C}} \right)}$$" /> and their Euclidean Counterparts