Year: 2025
Type: article
Abstract: Based on well-known heuristic arguments that provide an upper bound for the relaxation time of zero-range processes and trying to establish a connection between the results obtained in Landim et al. (Ann Probab 24(4), 1996), Morris (Ann Probab 34(5):1645–1664, 2006) and Nagahata (Stoch Process Appl 120(6):949–958, 2010) we proposed to study the zero-range process associated with the following family of rate functions: $$\begin{aligned} g_{\alpha }(k) = {\left\{ \begin{array}{ll} \frac{(k+1)^{1-\alpha }-1}{1-\alpha } & \text {if}\ \alpha \in [0,1) \cup (1,\infty ) \\ \ln (k+1) & \text {if}\ \alpha =1. \end{array}\right. } \end{aligned}$$ g α ( k ) = ( k + 1 ) 1 - α - 1 1 - α if α ∈ [ 0 , 1 ) ∪ ( 1 , ∞ ) ln ( k + 1 ) if α = 1 . We state a conjecture about the order of the relaxation time for those processes and provide numerical evidence throughout deterministic iterative methods and Monte-Carlo simulations.
Source: SeMA Journal
Authors: F. Hernández-Romero, M. Jara, F. Valentim
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,390
Funder: Universidad Nacional de Colombia
OpenAlex ID: W4410075632