Mixing
![Why are logics related to lattices and algebras? What can be said about this relationship? [closed]](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZCTB4-bb-s-32SAm6ytjzFOU06cH9o8q-a_wq_UnH6lcd8hvws23CmBWHM6g256LzTX9yK1EiCCzTC1NSgtxlNk_J9hdr9bA3tD0Nqntbl521j4bLAm_uXPANuWLBhcCKTKzns2gaUodx/s72-c/1.jpg)
Dynamical (or Master) equation for remove-replace process
Clash Royale CLAN TAG#URR8PPP
up vote
1
down vote
favorite
My question concerns a special kind of dynamical process. The setup is the following: We are given a Matrix $xi_mu^i in mathbbR^MxN$ which is initially chosen randomly (with entries from $mathcalN(0,1)$). We are also given a vector $p_i in mathbbR^N$, initialised randomly.
The process I am studying is the following: I compute the dot product $vecxi_mu cdot vecp$ and check whether
beginequation
vecxi_mu cdot vecp geq sigma qquad forall mu,
endequation
with $sigma in mathbbR$.
If the condition is not satisfied for the $mu$th vector $vecxi_mu$, I remove this vector and replace it with a new vector chosen randomly from the distribution $mathcalN (0,1)$
This process is what I call "remove and replace". I would like to know whether this dynamical process can be modeled by some kind of master equation (or any other stochastic differential equation) or not. What I am interested in is to understand how long-time limit (understood as performing this remove and replace procedure for a large number of times) depends on $sigma$.
I am not an expert on stochastic processes or master equations. So any help/pointers/criticisms are welcome. Thank you.
probability discrete-mathematics stochastic-processes dynamical-systems random-matrices
asked Aug 1 at 13:55
bfg
304
add a comment |Â
up vote
1
down vote
favorite
My question concerns a special kind of dynamical process. The setup is the following: We are given a Matrix $xi_mu^i in mathbbR^MxN$ which is initially chosen randomly (with entries from $mathcalN(0,1)$). We are also given a vector $p_i in mathbbR^N$, initialised randomly.
The process I am studying is the following: I compute the dot product $vecxi_mu cdot vecp$ and check whether
beginequation
vecxi_mu cdot vecp geq sigma qquad forall mu,
endequation
with $sigma in mathbbR$.
If the condition is not satisfied for the $mu$th vector $vecxi_mu$, I remove this vector and replace it with a new vector chosen randomly from the distribution $mathcalN (0,1)$
This process is what I call "remove and replace". I would like to know whether this dynamical process can be modeled by some kind of master equation (or any other stochastic differential equation) or not. What I am interested in is to understand how long-time limit (understood as performing this remove and replace procedure for a large number of times) depends on $sigma$.
I am not an expert on stochastic processes or master equations. So any help/pointers/criticisms are welcome. Thank you.
probability discrete-mathematics stochastic-processes dynamical-systems random-matrices
asked Aug 1 at 13:55
bfg
304
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
My question concerns a special kind of dynamical process. The setup is the following: We are given a Matrix $xi_mu^i in mathbbR^MxN$ which is initially chosen randomly (with entries from $mathcalN(0,1)$). We are also given a vector $p_i in mathbbR^N$, initialised randomly.
The process I am studying is the following: I compute the dot product $vecxi_mu cdot vecp$ and check whether
beginequation
vecxi_mu cdot vecp geq sigma qquad forall mu,
endequation
with $sigma in mathbbR$.
If the condition is not satisfied for the $mu$th vector $vecxi_mu$, I remove this vector and replace it with a new vector chosen randomly from the distribution $mathcalN (0,1)$
This process is what I call "remove and replace". I would like to know whether this dynamical process can be modeled by some kind of master equation (or any other stochastic differential equation) or not. What I am interested in is to understand how long-time limit (understood as performing this remove and replace procedure for a large number of times) depends on $sigma$.
I am not an expert on stochastic processes or master equations. So any help/pointers/criticisms are welcome. Thank you.
probability discrete-mathematics stochastic-processes dynamical-systems random-matrices
asked Aug 1 at 13:55
bfg
304
My question concerns a special kind of dynamical process. The setup is the following: We are given a Matrix $xi_mu^i in mathbbR^MxN$ which is initially chosen randomly (with entries from $mathcalN(0,1)$). We are also given a vector $p_i in mathbbR^N$, initialised randomly.
The process I am studying is the following: I compute the dot product $vecxi_mu cdot vecp$ and check whether
beginequation
vecxi_mu cdot vecp geq sigma qquad forall mu,
endequation
with $sigma in mathbbR$.
If the condition is not satisfied for the $mu$th vector $vecxi_mu$, I remove this vector and replace it with a new vector chosen randomly from the distribution $mathcalN (0,1)$
This process is what I call "remove and replace". I would like to know whether this dynamical process can be modeled by some kind of master equation (or any other stochastic differential equation) or not. What I am interested in is to understand how long-time limit (understood as performing this remove and replace procedure for a large number of times) depends on $sigma$.
I am not an expert on stochastic processes or master equations. So any help/pointers/criticisms are welcome. Thank you.
probability discrete-mathematics stochastic-processes dynamical-systems random-matrices
asked Aug 1 at 13:55
bfg
304
edited Aug 1 at 14:22
asked Aug 1 at 13:55
bfg
304
asked Aug 1 at 13:55
bfg
304
asked Aug 1 at 13:55
bfg
304
304
add a comment |Â
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2869098%2fdynamical-or-master-equation-for-remove-replace-process%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password