I guess you could call that an “investigation,” although it feels weird to me. By “on my own,” he has to be referring to sanctions power. He has no authority to just go a-sleuthing. “Outside of this trial” means he’s not going to disrupt trial proceedings with an order to show cause, even though he could, because some of the sanctions available to him include things that would immediately impact this trial (from a mandatory inference jury instruction up to default judgment).
I guess you could call that an “investigation,” although it feels weird to me. By “on my own,” he has to be referring to sanctions power. He has no authority to just go a-sleuthing. “Outside of this trial” means he’s not going to disrupt trial proceedings with an order to show cause, even though he could, because some of the sanctions available to him include things that would immediately impact this trial (from a mandatory inference jury instruction up to default judgment).