The Longtime Behavior Of Branching Random Walk In A Catalytic Medium
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چکیده
c J o u r n a l o f P r o b a b il ity A. G reven M athem ati sches Insti tut,U ni versi t at Erl angen{N urnberg, B i sm arckstrae 1 1/2,D-91054 Erl angen,G erm any A .K lenke M athem ati sches Insti tut,U ni versi t at Erl angen{N urnberg, B i sm arckstrae 1 1/2,D-91054 Erl angen,G erm any A. W akolbinger Fachberei ch M athem ati k,U ni versi t at Frankfurt, R obert{M ayer{Strae 6-10,D-60325 Frankfurt,G erm any A bstract W e consi der catal yti c branchi ng random w al k (the reactant) w here the state space i s a countabl e A bel ean group. T he branchi ng i s cri ti calbi nary and the l ocalbranchi ng rate i s gi ven by a catal yti c m edi um. H ere the m edi um i s i tsel fan autonom ous (ordi nary) branchi ng random w al k (the catal yst) { m aybe w i th a di erent m oti on l aw. For persi stent catal yst (transi ent m oti on) the reactant show s the usualdi chotom y ofpersi s-tence versus exti ncti on dependi ng on transi ence or recurrence ofi ts m oti on. If the catal yst goes to l ocalexti ncti on i t turns out that the l ongti m e behavi our of the re-actant ranges (dependi ng on i ts m oti on) from l ocalexti ncti on to free random w al k w i th ei ther determ i ni sti c or random gl obali ntensi ty ofparti cl es. K eyw ords B ranchi ng random w al k i n random m edi um ,reactant{catal ystsystem s,i nteracti ng parti cl e system s,random m edi a.
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