  SrRuO$_3$ presents a rare example of ferromagnetism among the 4$d$ based
oxides. While the nature of magnetic state in SrRuO$_3$ is mostly believed to
be of itinerant type, recent studies suggest a coexistence of both itinerant
and localized model of magnetism in this material. Here, we have investigated
the evolution of magnetic state in doped SrRu$_{1-x}$Ti$_x$O$_3$ through
studying the critical behavior using standard techniques such as, modified
Arrott plot, Kouvel-Fisher plot and critical isotherm analysis across the
magnetic transition temperature $T_c$. The substitution of nonmagnetic
Ti$^{4+}$ (3$d^{0}$) for Ru$^{4+}$ (4$d^4$) would simply dilute the magnetic
system apart from modifying the electron correlation effect and the density of
states at Fermi level. Surprisingly, $T_c$ does not change with $x$. Moreover,
our analysis show the exponent $\beta$ related to spontaneous magnetization
increases while the exponents $\gamma$ and $\delta$ related to initial inverse
susceptibility and critical magnetization, respectively decrease with Ti
substitution. The estimated exponents do not match with any established
theoretical models for universality classes, however, the exponent obey the
Widom relation and the scaling behavior. Interestingly, this particular
evolution of exponents in present series has similarity with that in
isoelectronic doped Sr$_{1-x}$Ca$_x$RuO$_3$. We believe that site dilution by
Ti leads to formation magnetic clusters which causes this specific changes in
critical exponents.
