The Packing Measure of the Range of Super-Brownian Motion
Thomas Duquesne

TL;DR
This paper establishes an exact packing measure for the total range of Super-Brownian motion in dimensions five and higher, linking the occupation measure to a specific gauge function with a precise constant.
Contribution
It provides a rigorous proof that the total occupation measure of Super-Brownian motion equals its $g$-packing measure with a dimension-dependent constant in super-critical dimensions.
Findings
The total range has an exact packing measure with respect to a specific gauge function.
The occupation measure equals the $g$-packing measure up to a constant.
The result applies in super-critical dimensions $d \,\geq\, 5$.
Abstract
We prove that the total range of Super-Brownian motion with quadratic branching mechanism has an exact packing measure with respect to the gauge function in super-critical dimensions . More precisely, we prove that the total occupation measure of Super-Brownian motion is equal to the -packing measure restricted to its range, up to a deterministic multiplicative constant that only depends on space dimension .
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