Large-range constant threshold growth model in one dimension [Elektronski vir]
Šega, Gregor
V članku opišemo enorazsežni model rasti s konstantnim pragom. Dinamika ima dva parametra, velikost okolice ▫$n$▫ ter prag ▫$\vartheta$▫. Nezasedena točka ▫$x$▫ postane zasedena z intenziteto 1, čim ...je v njeni okolici ▫$[x-n, x+n]$▫ vsaj ▫$\vartheta$▫ zasedenih točk. Ko ▫$n$▫ večamo, lahko dinamiko aproksimiramo z modelom v zveznem prostoru, ki ima eksplicitno izraženo invariantno porazdelitev v čelni okolici. Od tod dokažemo, da je hitrost širjenja zasedene množice asimptotično enaka ▫$\frac{n2}{2\vartheta}$▫.
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