Year: 2025
Type: article
Abstract: This article provides a scaling limit for a family of skew interacting Brownian motions in the context of mesoscopic interface models. Let $$M,d\in \mathbb {N}$$ M , d ∈ N , $$y_1,\dots ,y_M\in \mathbb {R}$$ y 1 , ⋯ , y M ∈ R , $$f\in C_b(\mathbb {R})$$ f ∈ C b ( R ) . For $$N\in \mathbb {N}$$ N ∈ N we consider a $$k_N$$ k N -dimensional, skew reflecting distorted Brownian motion $$(X^{N,i}_t)_{i=1,\dots ,k_N}$$ ( X t N , i ) i = 1 , ⋯ , k N , $$t\ge 0$$ t ≥ 0 , and investigate its scaling limit for $$N\rightarrow \infty $$ N → ∞ . The drift includes skew reflections at height levels $$\tilde{y}_j:=N^{1-\frac{d}{2}}y_j$$ y ~ j : = N 1 - d 2 y j with intensities $$\beta _j/N^d$$ β j / N d for $$j=1,\dots ,M$$ j = 1 ,
Source: Potential Analysis
Authors: Martin Grothaus, Simon Wittmann
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Awards: G2431417380, G7578079922
OpenAlex ID: W6921794855