<s>
Free	B-Algorithm
convolution	I-Algorithm
is	O
the	O
free	O
probability	O
analog	O
of	O
the	O
classical	O
notion	O
of	O
convolution	B-Language
of	O
probability	O
measures	O
.	O
</s>
<s>
Due	O
to	O
the	O
non-commutative	O
nature	O
of	O
free	O
probability	O
theory	O
,	O
one	O
has	O
to	O
talk	O
separately	O
about	O
additive	O
and	O
multiplicative	O
free	B-Algorithm
convolution	I-Algorithm
,	O
which	O
arise	O
from	O
addition	O
and	O
multiplication	O
of	O
free	O
random	O
variables	O
(	O
see	O
below	O
;	O
in	O
the	O
classical	O
case	O
,	O
what	O
would	O
be	O
the	O
analog	O
of	O
free	O
multiplicative	O
convolution	B-Language
can	O
be	O
reduced	O
to	O
additive	O
convolution	B-Language
by	O
passing	O
to	O
logarithms	O
of	O
random	O
variables	O
)	O
.	O
</s>
<s>
The	O
notion	O
of	O
free	B-Algorithm
convolution	I-Algorithm
was	O
introduced	O
by	O
Voiculescu	O
.	O
</s>
<s>
Then	O
the	O
free	O
additive	O
convolution	B-Language
is	O
the	O
law	O
of	O
.	O
</s>
<s>
The	O
rectangular	O
free	O
additive	O
convolution	B-Language
(	O
with	O
ratio	O
)	O
has	O
also	O
been	O
defined	O
in	O
the	O
non	O
commutative	O
probability	O
framework	O
by	O
Benaych-Georges	O
and	O
admits	O
the	O
following	O
random	O
matrices	O
interpretation	O
.	O
</s>
<s>
Then	O
the	O
free	O
multiplicative	O
convolution	B-Language
is	O
the	O
law	O
of	O
(	O
or	O
,	O
equivalently	O
,	O
the	O
law	O
of	O
.	O
</s>
<s>
Explicit	O
computations	O
of	O
multiplicative	O
free	B-Algorithm
convolution	I-Algorithm
can	O
be	O
carried	O
out	O
using	O
complex-analytic	O
techniques	O
and	O
the	O
S-transform	O
.	O
</s>
<s>
Free	B-Algorithm
convolution	I-Algorithm
can	O
be	O
used	O
to	O
give	O
a	O
proof	O
of	O
the	O
free	O
central	O
limit	O
theorem	O
.	O
</s>
<s>
Free	B-Algorithm
convolution	I-Algorithm
can	O
be	O
used	O
to	O
compute	O
the	O
laws	O
and	O
spectra	O
of	O
sums	O
or	O
products	O
of	O
random	O
variables	O
which	O
are	O
free	O
.	O
</s>
<s>
Through	O
its	O
applications	O
to	O
random	O
matrices	O
,	O
free	B-Algorithm
convolution	I-Algorithm
has	O
some	O
strong	O
connections	O
with	O
other	O
works	O
on	O
G-estimation	O
of	O
Girko	O
.	O
</s>
