Law of large numbers and fluctuations in the sub-critical and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e20" altimg="si3.svg"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> regions for SHE and KPZ equation in dimension <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e30" altimg="si4.svg"><mml:mrow><mml:mi>d</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="…
Stochastic processes and their applications