-Pisot numbers in any real algebraic number field are relatively dense

An algebraic integer is called an -Pisot number ( >0) if its Galois conjugates have absolute value less then . Let K be any real algebraic number field. We prove that the subset of K consisting of -Pisot numbers which have the same degree as that of the field is relatively dense in the real line . This has some applications to non-stationary products of random matrices involving Salem numbers.