arXiv subjects

Arthur Dremaux

Publications and source records attributed to Arthur Dremaux.

3 recordsLinked to original sources

arXiv2026

A one-parameter family of local-time conditioned processes : the generalized Brownian burglars

We construct and characterize the one-parameter family of real-valued processes that allow to recover the law of a Brownian loop-soup of any intensity on the real line conditionally on its occupation time field. These processes generalize the Brownian burglar constructed by Warren and Yor (that corresponds to our process in the limiting case where the intensity vanishes and there is just one Brownian motion). These processes are closely related to the Bass-Burdzy flow and recent work of A\"id\'ekon, Hu and Shi on the stochastic Jacobi flow. Our approach uses a formalism, building on the notion of driver processes, where one considers the evolving object to be the line that we ``stretch", instead of the burglar itself and its remaining occupation time. This leads to a characterization of these (generalized) Brownian burglars by simple natural axioms. It also allows to treat ``negative intensities'' and provides fairly direct derivations of several properties of the burglars, and in particular a ``target-independence/locality" property at the special intensity where the local time is the square of a Gaussian Free Field.

math.PR↗

arXiv2025

Singularity of the loops within a cable-graph loop-soup conditioned by its occupation time

In this note, we show the following feature of the relation between Brownian loop-soups on cable-graphs and their total occupation time-field $\Lambda$: When conditioned on $\Lambda$, the conditional law of individual loops becomes singular with respect to that of unconditioned loops. The idea of the proof is to see that some type of fast points on the curve $\Lambda$ impose an exceptional behaviour of all the loops when they go through these points.

math.PR↗

arXiv2023

How the Move Acceptance Hyper-Heuristic Copes With Local Optima: Drastic Differences Between Jumps and Cliffs

In recent work, Lissovoi, Oliveto, and Warwicker (Artificial Intelligence (2023)) proved that the Move Acceptance Hyper-Heuristic (MAHH) leaves the local optimum of the multimodal cliff benchmark with remarkable efficiency. With its $O(n^3)$ runtime, for almost all cliff widths $d,$ the MAHH massively outperforms the $\Theta(n^d)$ runtime of simple elitist evolutionary algorithms (EAs). For the most prominent multimodal benchmark, the jump functions, the given runtime estimates of $O(n^{2m} m^{-\Theta(m)})$ and $\Omega(2^{\Omega(m)})$, for gap size $m \ge 2$, are far apart and the real performance of MAHH is still an open question. In this work, we resolve this question. We prove that for any choice of the MAHH selection parameter~$p$, the expected runtime of the MAHH on a jump function with gap size $m = o(n^{1/2})$ is at least $\Omega(n^{2m-1} / (2m-1)!)$. This renders the MAHH much slower than simple elitist evolutionary algorithms with their typical $O(n^m)$ runtime. We also show that the MAHH with the global bit-wise mutation operator instead of the local one-bit operator optimizes jump functions in time $O(\min\{m n^m,\frac{n^{2m-1}}{m!\Omega(m)^{m-2}}\})$, essentially the minimum of the optimization times of the $(1+1)$ EA and the MAHH. This suggests that combining several ways to cope with local optima can be a fruitful approach.

cs.NE↗