Composition with a two variable function
We compute the motivic nearby cycles of functions obtained by composition of two functions with distinct sets of variables with a two variable function
math.AG↗
arXiv subjects
M. Merle
Publications and source records attributed to M. Merle.
On the occupation measure of super-Brownian motion
We derive the asymptotic behavior of the occupation measure of the unit ball, for super-Brownian motion started from the Dirac measure at a distant point x and conditioned to hit the unit ball. In the critical dimension d=4, we obtain a limiting exponential distribution for the ratio of the occupation measure over log(|x|).
math.PR↗
Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of Steenbrink
Using iterated vanishing cycles and convolution, we prove a motivic version of a conjecture of Steenbrink concerning the spectrum of hypersurface singularities
math.AG↗
Nearby cycles and composition with a non-degenerate polynomial
We compute the motivic nearby cycles of functions obtained by composition with a polynomial which is non-degenerate with respect to its Newton polyhedron. Our result involves new convolution operators and generalized nearby cycles.
math.AG↗