so let us discussan interesting question on
how do people occupy houses in a locality
so assume you had a few houses and you want
to choose a house for yourself what kind of
house will you like living in that you think
who your neighbours are matters to some extent
would you like to be in a locality where your
neighbours aresomeone with whom you cannot
have a conversation or your neighborhood is
full of people who are unlike you would you
like staying in such locality
now here is an observation made several times
in theliterature the observation is people
are known to go and occupy a place a locality
or a city uniformly at random but which time
they sort of start segregated by segregating
i mean they all get together you will see
clusters of different types of people here
is a type of people lets call it type green
they all are together they all are together
and there is this type red as well they all
are together to they you can see the clustering
happening here they wish to stay with each
other people have observed why exactly this
happens as i told you this is not observed
initially initially they come and occupy the
place uniformly at random but which time you
see this kind of segregation that i am showing
here
they get segregated into different classes
so assume in the united states you will see
a lot of indians chinese and people fromotherah
countries but you will see that indian tend
to sort ofstaywith each other in in colonies
and there will be colonies of chinese as wellalthough
there will be some sort of mingling butthere
are places where you will see only people
of one type ok this is observed in many places
soassume you were to live in a foreign country
or even in your own country would you not
like to live in a place where you are surrounded
by people who are of your type now this is
observed and let us assume you are surrounded
by people who are not like you it is observed
that people then they came to migrate
this is you and your surrounded by people
who are unlike you what will happened nobody
would like to stay in such a place would you
like to stay in such a place absolutely not
mostly not but then would you not prefer to
stay theyyour type of people are present right
so people people who are around you are all
like you anybody would like to stay in such
a place not just this in fact at least some
of them should be like you right at least
some of them should be like you for example
you are here and you are surrounded by at
least some three people who are like and the
other one two three four five people are not
like you you wouldnt care much
so let us call this the threshold value t
equals three which means whenever take a pos
and understand what i am saying this is the
important concept in this lecture wherever
you are surrounded by at least t number of
people out of eight people who can surround
you in a neighborhood three behind three in
the front and two people on a sideways lets
say at least when you have t number of people
who are like you then you will stay there
if they are not if you are not surrounded
by people at least t people who are like you
then you will migrate here are three people
who are like me and my threshold is actually
three so i like living in such a neighborhood
so it is believed that unhappy people change
their house to a happier destination by unhappy
people i mean people who are surrounded by
less than t number of people in the previous
case we saw t was three which means this fellow
was happy if in case this particular thing
instead of being green was red then he would
be unhappy because is neighbours would be
less than three ok can we model this as a
question can this be modeled can we model
and see what exactly happens when people are
unhappy and they migrate they come and occupy
place uniformly at random a house uniformly
at random in a city and then later they realize
that because of the neighborhood they want
to move to some other place
how do we model this there is a very popular
model called the schelling model its a very
interesting modelvery simple and straight
forward simulation it goes like this we assume
that a grid simulatescity gridah is aanalog
to a city and we simulate the behaviour of
people how do we do that we take a grid like
this and then we put a into for one parity
that is lets say type green and then oh for
a red parity type red ok so this particular
person x is surrounded byah the four red people
andfour green people as i told you if the
threshold is three then this green fellow
is actually happy ok
now let us take a look at on online simulation
of the schellings model what is schillings
model say schillings model simply says that
as and when people are unhappy because they
are surrounded byneighbours below their threshold
value what do i mean by that sounds a little
all i am trying to say is my threshold is
three or may be two if i have two people in
my neighborhood who are of my type i will
stay there otherwise i will move let me take
a big grid and then try simulating this and
seeing let us see what one can observe there
are a lot of online simulations of this model
i am just going to open a browser right now
and then i am going to show you one such simulation
